NEWSLETTER No. 42

December 2001

EMS Agenda ................................................................................................. 2

Editorial Thomas Hintermann .................................................................. 3

Executive Committee Meeting Berlin ......................................................... 4

EMS Council Elections .................................................................................. 8

New Members .............................................................................................. 10

Anniversaries Pierre de Fermat by Klaus Barner .................................... 12

Interview with Sergey P. Novikov ............................................................... 17

Obituary Jacques-Louis Lions .................................................................. 21

Ukrainian Mathematical Congress ............................................................. 26

Forthcoming Conferences ............................................................................ 29

Recent Books ............................................................................................... 34

Designed and printed by Armstrong Press LimitedCrosshouse Road, Southampton, Hampshire SO14 5GZ, UK

telephone: (+44) 23 8033 3132 fax: (+44) 23 8033 3134Published by European Mathematical Society

ISSN 1027 - 488X

The views expressed in this Newsletter are those of the authors and do not necessarilyrepresent those of the EMS or the Editorial team.

NOTICE FOR MATHEMATICAL SOCIETIESLabels for the next issue will be prepared during the second half of February 2002.Please send your updated lists before then to Ms Tuulikki Mäkeläinen, Department ofMathematics, P.O. Box 4, FIN-00014 University of Helsinki, Finland; e-mail:makelain@cc.helsinki.fi

INSTITUTIONAL SUBSCRIPTIONS FOR THE EMS NEWSLETTERInstitutes and libraries can order the EMS Newsletter by mail from the EMS Secretariat,Department of Mathematics, P. O. Box 4, FI-00014 University of Helsinki, Finland, or by e-mail: (makelain@cc.helsinki.fi). Please include the name and full address (with postal code),telephone and fax number (with country code) and e-mail address. The annual subscription fee(including mailing) is 65 euros; an invoice will be sent with a sample copy of the Newsletter.

EDITOR-IN-CHIEFROBIN WILSONDepartment of Pure MathematicsThe Open UniversityMilton Keynes MK7 6AA, UKe-mail: r.j.wilson@open.ac.uk

ASSOCIATE EDITORSSTEEN MARKVORSENDepartment of Mathematics Technical University of DenmarkBuilding 303DK-2800 Kgs. Lyngby, Denmarke-mail: s.markvorsen@mat.dtu.dkKRZYSZTOF CIESIELSKIMathematics Institute Jagiellonian UniversityReymonta 4 30-059 Kraków, Polande-mail: ciesiels@im.uj.edu.plKATHLEEN QUINNThe Open University [address as above]e-mail: k.a.s.quinn@open.ac.uk

SPECIALIST EDITORSINTERVIEWSSteen Markvorsen [address as above]SOCIETIESKrzysztof Ciesielski [address as above]EDUCATIONTony GardinerUniversity of BirminghamBirmingham B15 2TT, UKe-mail: a.d.gardiner@bham.ac.ukMATHEMATICAL PROBLEMSPaul JaintaWerkvolkstr. 10D-91126 Schwabach, Germanye-mail: PaulJainta@aol.com ANNIVERSARIESJune Barrow-Green and Jeremy GrayOpen University [address as above]e-mail: j.e.barrow-green@open.ac.ukand j.j.gray@open.ac.uk andCONFERENCESKathleen Quinn [address as above]RECENT BOOKSIvan Netuka and Vladimir Sou³ekMathematical InstituteCharles UniversitySokolovská 8318600 Prague, Czech Republice-mail: netuka@karlin.mff.cuni.czand soucek@karlin.mff.cuni.czADVERTISING OFFICERVivette GiraultLaboratoire dAnalyse NumériqueBoite Courrier 187, Université Pierre et Marie Curie, 4 Place Jussieu75252 Paris Cedex 05, Francee-mail: girault@ann.jussieu.frOPEN UNIVERSITY PRODUCTION TEAMLiz Scarna, Kathleen Quinn

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CONTENTS

EMS December 2001

EDITORIALTEAM EUROPEAN MATHEMATICAL SOCIETY

EXECUTIVE COMMITTEEPRESIDENT (19992002)Prof. ROLF JELTSCHSeminar for Applied MathematicsETH, CH-8092 Zürich, Switzerlande-mail: jeltsch@sam.math.ethz.chVICE-PRESIDENTSProf. LUC LEMAIRE (19992002)Department of Mathematics Université Libre de BruxellesC.P. 218 Campus PlaineBld du TriompheB-1050 Bruxelles, Belgiume-mail: llemaire@ulb.ac.beProf. BODIL BRANNER (20012004)Department of MathematicsTechnical University of DenmarkBuilding 303DK-2800 Kgs. Lyngby, Denmarke-mail: bbranner@mat.dtu.dkSECRETARY (19992002)Prof. DAVID BRANNANDepartment of Pure Mathematics The Open UniversityWalton HallMilton Keynes MK7 6AA, UKe-mail: d.a.brannan@open.ac.ukTREASURER (19992002)Prof. OLLI MARTIODepartment of MathematicsP.O. Box 4FIN-00014 University of HelsinkiFinlande-mail: olli.martio@helsinki.fi ORDINARY MEMBERSProf. VICTOR BUCHSTABER (20012004)Department of Mathematics and MechanicsMoscow State University119899 Moscow, Russiae-mail: buchstab@mendeleevo.ru Prof. DOINA CIORANESCU (19992002)Laboratoire dAnalyse NumériqueUniversité Paris VI4 Place Jussieu75252 Paris Cedex 05, Francee-mail: cioran@ann.jussieu.frProf. RENZO PICCININI (19992002)Dipartimento di Matematica e ApplicazioniUniversità di Milano-BicoccaVia Bicocca degli Arcimboldi, 820126 Milano, Italye-mail: renzo@matapp.unimib.itProf. MARTA SANZ-SOLÉ (19972000)Facultat de MatematiquesUniversitat de BarcelonaGran Via 585E-08007 Barcelona, Spaine-mail: sanz@cerber.mat.ub.esProf. MINA TEICHER (20012004)Department of Mathematics and Computer ScienceBar-Ilan UniversityRamat-Gan 52900, Israele-mail: teicher@macs.biu.ac.il EMS SECRETARIATMs. T. MÄKELÄINENDepartment of MathematicsP.O. Box 4FIN-00014 University of HelsinkiFinlandtel: (+358)-9-1912-2883fax: (+358)-9-1912-3213telex: 124690e-mail: makelain@cc.helsinki.fiwebsite: http://www.emis.de

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EMS NEWS

EMS December 2001

20029-10 FebruaryEMS Executive Committee Meeting in Brussels (Belgium), at the invitationof the Belgian Mathematical Society and the Université Libre de Bruxelles

15 February Deadline for submission of material for the March issue of the EMSNewsletterContact: Robin Wilson, e-mail: r.j.wilson@open.ac.uk

24-28 February EMS Summer School in Eilat (Israel)Title: Algebraic Geometry, Computations and ApplicationsContact: Mina Teicher, e-mail: teicher@macs.biu.ac.il

1 MarchDeadline for Proposals for 2003 EMS Lectures Contact: David Brannan, e-mail: d.a.brannan@open.ac.uk

15 MayDeadline for submission of material for the June issue of the EMS NewsletterContact: Robin Wilson, e-mail: r.j.wilson@open.ac.uk

19-31 MayEMS Summer School in Craiova (Romania)Title: Mathematical and numerical methods in computational quantum chemistryContact: Yvon Maday, e-mail: maday@ann.jussieu.fr

31 May Executive Committee meeting in Oslo (Norway)

1-2 June EMS Council Meeting, Oslo

3-8 JuneAbel Bicentennial Conference, Oslo

28-29 SeptemberExecutive Committee meeting in Stockholm (Sweden)

200310-13 FebruaryEMS-SMAI-SMF Meeting in Nice (France)Title: Mathématiques Appliquées - Applications des Mathématiques (AppliedMathematics - Applications of Mathematics)Contacts: Doina Cioranescu and Mireille Martin-Deschamps, e-mail: cioran@ann.jussieu.fr and mmd@math.uvsq.fr

200425-27 June EMS Council Meeting, Stockholm (Sweden)

27 June - 2 July4th European Congress of Mathematics, Stockholm

EMS AgendaEMS Committee

The idea for the EMS to engage in pub-lishing activities is probably almost as oldas the society itself. It resulted, mostnotably, in the creation in 1999 of JEMS,the Journal of the European MathematicalSociety, currently published on behalf of theEMS by Springer-Verlag, now a member ofthe Bertelsmann Springer group. Justabout the same time, the first serious plansemerged to run a commercially operatingpublishing house. Among the availableoptions, including taking over an indepen-dent publisher or combining the efforts ofmember society publishers, the EMS even-tually decided to launch their own enter-prise. Although this possibility hadalready been hinted at in the EMSNewsletter, the intention was first communi-cated to a large audience by the EMSPresident, Rolf Jeltsch, during his speechat the closing ceremony of the ECM inBarcelona in July 2000. In the interim,much energy has been spent on the legalaspects of the undertaking, hopefully cul-minating in the registration of theEuropean Mathematical Foundation, thegoverning body of the EMS publishinghouse, with the Swiss chamber of com-merce in late 2001.

An increasing proportion of the mathe-matical community is dissatisfied with themathematical publishing industry. Aboveall, it is the pricing policy of some largeand important commercial publishers thatis under debate, and there is a general feel-ing that they hinder the dissemination ofmathematical knowledge rather than fos-ter it. Be that as it may, there is certainlyno denying that at present the order of theday in every company is to meet short-term(short-sighted?) targets, most often at theexpense of everything else. Financial con-siderations are clearly given first priority,and editorial matters and publishingaspects rank second. One of the aims ofthe EMS publishing house is to reverse thatorder. The needs of the community areforemost in our minds, admittedly with theobligation to run an economically soundoperation.

I do not share the view that scientificinformation should be entirely free. Toquote John Ewing of the AmericanMathematical Society, nothing is for freeand the question is only who is paying.The collecting, editing and publishing ofscientific content will always entail labourthat belongs in the hands of professionals,rather than of scientists who should be ableto devote themselves to research andteaching. Such a sharing of responsibilitiesis effective and in the interest of us all.Rather than depending on external fund-ing, on volunteers, and on direct or indi-rect support from University institutions,we believe that financial independence is

the best option for long-term sustainabili-ty. In other words, our publications willnot be free, but available at the minimal

price possible under market conditions.Everything spent on them will be fullyreinvested in the publishing house. Withthe purchase of a book or the subscriptionof a journal you will support an endeavourthat has your interests in mind. No pay-ments are made to shareholders, and anyprofits have to be used on aims set down inthe statutes of the Foundation.

We expect that the first publications ofthe EMS to appear under their own namewill be published at the beginning of 2004,possibly earlier. We intend to publish first-quality peer-reviewed journals, and bookson all academic levels and from all fields ofmathematics, emphatically includingapplied mathematics. Proposals are wel-come and should be submitted to theaddress below. We appeal to all mathe-maticians to support our effort by publish-ing with us, and by endorsing the subscrip-tion of our journals and the purchase ofour books by the library of your homeinstitution. We promise to pay back yourconfidence with the best possible serviceand quality.

Although the EMF is legally a separatestructure from the EMS, the statutes andby-laws of the foundation ensure the deci-sive influence of the EMS, through the par-ticipation of committee members in theboard of trustees. Moreover, the editorialboards of our journals and book series willconsist of mathematicians approved by,and sympathetic with, the aims of the EMS.

You will be informed on the progress ofour plans in the EMS Newsletter. Apartfrom the creation of its own publishing

house, the EMS continues to offer a largeand well-maintained collection of non-commercial journals and books on EMIS,the European Mathematics InformationService (www.emis.de).Dr. Thomas Hintermann is at the Department ofApplied Mathematics, ETH-Zentrum FLI C1, CH-8092 Zürich, Switzerland; e-mail: hintermann@math.ethz.chtel:+41 1 632 34 36, fax +41 1 632 11 04

EDITORIAL

EMS December 2001 3

EditorialEditorialThomas Hintermann

(Publishing Director, EMS Publishing Division)

The Citation Checker andCross Reference LinkGenerator offered byZentralblatt MATH

Bernd Wegner

For quite a long time ZentralblattMATH has offered the facility forexporting BIBTEX-files to usersmachines from the hit list obtained byretrieving information from theZentralblatt MATH database. This hasturned out to be a useful tool forauthors preparing a list of referencesfor their articles. Responding to fre-quent demand, Zentralblatt MATH nowprovides an additional new service, inorder to allow you to check your arti-cle literature references convenientlyand quickly, and to provide persistentlinks to individual Zentralblatt MATHdatabase items. This tool is freelyavailable and will be soon extended tothe Jahrbuch database.

The search menu for the citationchecker is available under the URLhttp://www.emis.de/ZMATH/x-ref.html.Users will be requested to enter infor-mation on the citation item in fourfields: last name of (first) author, sig-nificant word in the title, volume num-ber, first page. This will be sufficientin nearly all cases to pinpoint the sin-gle item looked for in particular,when all four fields are used. In therather unlikely case that more thanthree items match the search criteria,the most recent three items are dis-played. If the requested item does notbelong to them, then the standardretrieval forms for Zentralblatt MATHmay provide further help for thosewho have a subscription to this service.

The search result will offer precisestandardised bibliographic data, to beexported by the user into his own ref-erencing system. The addition of theZentralblatt MATH annotation numberwill add a unique identifier for thearticle, which will be suitable as a per-sistent link to the electronic offer ofthis publication and may serve as atool for reference linking going to awider range than provided by DOI, forexample.Bernd Wegner, TU Berlin, Fakultät II,Institut für Mathematik, 10623 Berlin,Germany; e-mail: wegner@math.tu-berlin.de

Thomas Hintermann

Present: Rolf Jeltsch (President, in theChair), David Brannan, Bodil Branner,Victor Buchstaber, Doina Cioranescu, LucLemaire, Olli Martio, Renzo Piccinini,Marta Sanz-Sole and Mina Teicher; (byinvitation) Carles Casacuberta, TuulikkiMakelainen, David Salinger and BerndWegner; (by invitation to part of the meet-ing) Peter Deuflhard, Tony Gardiner,Thomas Hintermann, Ari Laptev,Christian Mehl and Rudolf Straesser.

The President thanked Bernd Wegnerand Barbara Strazzabosco for the efficientand pleasant local arrangements.

Officers ReportsThe President sent a personal card of con-dolences to the family of J.-L. Lions. Aconference dedicated to J.-L. Lions will beheld at Collège de France, Paris, in July2002.

An Abel Prize has been established, withan endowment fund of 200,000,000 NOK,the annual yield covering the prize of300,000 annually.

A bid from the Swiss MathematicalSociety to hold ICIAM 2007 in Zürich wassuccessful. Rolf Jeltsch will be the localorganiser, and the EMS will be activelyinvolved.

Colette Laborde has been appointed tothe Education Committee, Chris Budd tothe RPA (Raising the Public Awareness ofMathematics) Committee, and KouliKyriaki to the Committee on Women andMathematics. The Euler InternationalMathematical Institute has been acceptedas a member of ERCOM (EuropeanResearch Centres in the MathematicalSciences).

There was a brief discussion of the newproposal for the 6th Framework Programmeof the European Union, which will be votedon in 2002. Networks andEuroconferences are included as fundable;it might also be possible to support activi-ties in EU-Associated States (these do notinclude Russia) in this way. It was felt thatthe EMS might set up a small office inBrussels to coordinate its EU-related activ-ities.

35 people had attended an EMSBrainstorming Weekend on AppliedMathematics in Berlingen on 4-6 May 2001.Rolf Jeltsch proposed a meeting to be heldin Berlingen in Spring 2002 to discusspublishing, meetings, EU funding formathematics conferences and integratedinitiatives. It was thought that societiestended to send high-quality people withreal commitment to such meetings.Several representatives of the EC wouldalso attend.

The Treasurer reported that the Societysfinances were under control. Expenditurein 2000 has been higher than average, dueto the Council meeting in Barcelona. The

costs of the Newsletter were quite highbecause of the strength of sterling againstthe euro.

A list of new individual EMS members(see later in this Newsletter) was approved.

ProjectsA report was received on the May meetingof the Zentralblatt für MathematikConsultative Committee in the headquartersof FIZ-Karlsruhe. The financial situationof Zentralblatt was improving. BerndWegner was praised for his work forZentralblatt, particularly in relation to theconsortia arrangements. The pricing forZentralblatt for the year 2002 had now beenagreed: there will be a slight increase inprices, with no lower price for the printedversion only. It was noted that theGerman government gives financial sup-

port to Zentralblatt and that more interna-tional financial help should be sought inthe future. The ownership of theZentralblatt title is shared between theEMS, FIZ, Springer and the HeidelbergAcademy of Science

A report on the LIMES (LargeInfrastructure in Mathematics - Enhanced

Services) project revealed that goodprogress had been achieved so far, and afirst release of new software would comeout soon.

A final report was received on theReference Levels for 16-year-olds project; theobjective has been to identify some com-mon standards for levels of understandingof mathematics across European countriesat the particular age of 16. A short con-ference on the project outcome had beenheld in Luxembourg, and it was plannedto hold a briefing in Brussels for EUCommission staff. There was a lengthydiscussion of a possible similar project for18-year-olds.

EMF/EMS Publishing HouseThe first meeting of the Board of Trusteesof the EMF (European MathematicalFoundation) had been held in Zürich inJuly, and a report of its discussions wasreceived by the Committee. The EMF is anot-for-profit trust that is the legal entityresponsible for the work of the newEMSph (European Mathematical SocietyPublishing House). Its Chair is Rolf Jeltsch,with Olli Martio as Treasurer, David

Brannan as Secretary and Eduard Zehnder(ETH) as the other trustee. The by-lawsand tax status of the EMF were discussedat the Board meeting.

EMF has appointed ThomasHintermann (formerly with Birkhäuser-Verlag, and with 12 years experience ofpublishing mathematics) as the launch

EMS NEWS

EMS December 20014

Executive Committee Meeting Executive Committee Meeting Berlin, 1-2 September 2001

Managing Director of EMSph, and he tookup his post on 1 September. In a wide-ranging briefing to the ExecutiveCommittee, Thomas Hintermann notedthat the rationale for the EMSph had beenthe widespread dissatisfaction of mathe-maticians with the work and prices ofmany commercial publishers. In addition,a regular income from publishing wouldhelp to give the EMS financial stability.His view was that there would always be aneed for publishers, as it is not a good useof mathematicians own time to divert itinto such technical and time-consumingmatters.

There was some daiscussion of the widerange of models for collaboration that theEMSph might follow, depending on indi-vidual negotiations with each proposedpartner. The EMSph would be active in

publishing journals, individual books andseries of books.

EMISThere was a discussion led by ChristianMehl and Volker Mehrmann on the pre-sent status of the left-hand side of EMIS.Arrangements were to be set up for ensur-ing that changes in the EMS committeememberships should appear on EMIS.

The idea of setting up some sort of jobinformation site on EMIS had proved animpossible task; it was thought that an e-letter (weekly or monthly) could be a bet-ter method for disseminating information,and that this could be discussed atBerlingen. Volker Mehrmann andChristian Mehl were thanked warmly fortheir work on EMIS.

ElibMThree journals had been made availablerecently on ElibM: Advances in Geometry (deGruyter), CMAM (Byelorussia) and AMEN(Taiwan). The installation of Annals ofMathematics was in hand, due to the effortsof Larry Siebenmann. The same privi-leges were given as for the arXiv. Therewould be no longer be a five years delay.The first years issues of JEMS would short-ly be made freely accessible on EMIS.

As announced previously, new develop-ments in the publication of commercialmathematical journals and the dominatingrole of electronic versions may force thedual journals in EMIS to charge for accessto the current electronic publications. For

these journals, such a possibility will bearranged on a separate server providingaccess control facilities; no charging willtake place on EMIS itself.

Electronic content with charged accesswill be made freely accessible in ElibM,after some period to be decided by eachindividual dual journal. During thecharged period, ElibM will provide freeaccess to bibliographic data and abstracts.Distribution of the metadata to the mirrorswill happen immediately after availability.The papers themselves will be given to themirrors as soon as they are freely available.

In relation to the archiving of electroniccontent, the authenticity of electronic ver-sions of papers will be an important issue.The CEIC (Committee on ElectronicInformation and Communication) hadbeen requested to develop a general rec-ommendation in the direction of fixing adate after which a paper could not be fur-ther altered without its becoming a sepa-rate publication.

In future, PDF files will be requested ascommon standard for ElibM, to provideeasier readability of the files. As a conse-quence of the large number of journals inElibM, access facilities to the content needto be improved, giving an alternative tojust clicking through contents. This willrequire more standardised delivery ofmetadata.

Linking references with electronic orretro-digitised versions is an importantquality issue for electronic publications.The journals in ElibM are likely to move tosuch an enhancement, and electronic doc-ument identifiers will be needed for this.

The DOI used by commercial publishersfor current electronic publications is a rel-atively expensive solution [DOI = DigitalObject Identifier, see http://www.doi.org]; itwill be possible to use the ZBL-annotationnumbers for this. There is an initiative toproduce a matching list between ZBL andMR annotations; for older items, theJahrbuch identifiers may be used. ZBL andthe AMS have agreed to create a matchinglist of identifiers for papers; this will becheaper than DOI.

EMIS has mirrors at SUB Göttingen andthe Cornell University Library; they wereinstalled for looking after later archivingof articles and books in EMIS. With morethan five years of electronic volumes avail-able for most journals in ELibM, archivingneeds to be established in a more system-atic way. This fits into a new initiativecalled EMANI (Electronic MathematicsArchiving Initiative), where SUBGöttingen and the Cornell UniversityLibrary are partners, in which the TeX-source codes and the PDF files are thebasis for archiving. This cooperationbetween libraries and journals will have tobe established in every single case, journalby journal, establishing a series of con-tracts.

Retro-digitising will improve the avail-ability of electronic offers in mathematics.Most dual journals in ELibM have suchextended offers already, thanks to partici-pation in the ERAM-project. These activi-ties are guided by SUB Göttingen and TU

Berlin, the latter represented by BerndWegner.

JSTOR offers more than 120 retro-digi-tised journals in science. Between 10 and20 of them offer a lot of mathematical con-tent. [JSTOR = Journal Storage. TheScholarly Journal Archive: seehttp://www.jstor.org or http://www.jstor.ac.uk].

EMANI (Electronic Mathematics ArchivingInitiative) is a cooperation between pub-lishers, editors and libraries, with the goalof caring about the long-term archivingand availability of electronic content inmathematics. The main contributors fromthe publishers side are Birkhäuser andSpringer-Verlag, but publications in ElibMmay also take part in this initiative. A starton the archiving will be made by theTsinghua University Library, the SUBGöttingen and the Cornell UniversityLibrary.

The Mathematical Heritage proposal

encourages mathematicians to make alltheir research papers available on the web.Martin Grötschel and Peter Michor bothhave proposals in this direction.

There will be a satellite conference ofICM 2002 on Electronic Information andCommunication in Mathematics at TsinghuaUniversity in Beijing; the organisers willbe Fengshan Bai and Bernd Wegner.ElibM and other projects in EMIS will beincluded among the subjects presentedthere. Details of the conference can befound on the ICM home page.

EMS CommitteesA new Chairman for the Committee onDeveloping Countries is being sought. It wasthought that the Committee might decideto look afresh at its terms of reference.

The composition of the Committee for theSupport for Eastern and Central EuropeanMathematicians was agreed as follows:Andrzej Pelczar (Chair), VictorBuchstaber, Martin Fuchs, MichelHazewinkel, George Jaiani, Laszlo Marki,Olli Martio and V.V. Sharko.

The topic of the Special EventsCommittees Fifth Diderot MathematicalForum (5DMF) on 22-23 November 2001,was to be Mathematics andTelecommunications, with special emphasison cellular phones. The cities and institu-tions involved would be: Philips Research(Eindhoven, Netherlands), Helsinki

EMS NEWS

EMS December 2001 5

Marta Sanz-Solé

Carles Casaculberta

University of Technology (Finland) andÉcole Polytechnique Federale deLausanne (Switzerland). The formatwould be as usual, with two days of meet-ings (their length will depend on the site)and three one-hour lectures (includingquestions) shared between all three sites.The lectures would be given by JoachimHagenauer (Technical University,Munich) in Eindhoven, Yrjo Neuvo(Nokia) in Helsinki, and Jacob Ziv(Technion Haifa) in Lausanne.

Two other events, which could lead to

special events that the EMS might take upas opportunities to celebrate the impact ofmathematics, are connected with the birthcentenaries of John von Neumann (in2002) and A.N. Kolmogorov (in 2003).The Special Events Committee wasencouraged to proceed with investigatingthese projects.

Saul Abarbanel (Israel) was elected tochair the Committee for Applied Mathematicsfor 2002-5; his subject area is numericalhyperbolic PDEs. It was felt essential thatall strands of applied mathematics shouldbe represented in this EMS committee,that corporate members should be consult-ed on its membership, that no memberhad a right to specify a member of thecommittee, and that there should alwaysbe adequate representation of appliedmathematics and of this committee on theEC.

It was agreed that the EMS SummerSchools Committee should write guidelinesfor potential organisers of EMS summerschools. These should indicate that thereare a limited number of speakers, that theduration is at most 2 weeks, that it can befor new postgraduates as well as for post-doctoral mathematicians, and it shouldoutline the differences between a confer-ence and a summer school.

The St Petersburg Summer School, 9-22July 2001, had been devoted to mathemat-ics and mathematical physics. The num-ber of participants had been 78, and theschool was considered a success. Financialsupport had been received from the EMS,UNESCO, NATO and the RussianFoundation for Basic Research. ItsProceedings will be published by Kluwerand Springer.

The Prague Summer School had 88 partic-ipants. Financing had been obtained fromthe Czech Republic, ESF, AMIF, theInternational Visegrad Fund, and a guar-antee of 2000 euro from the EMS; an

application to UNESCO-Roste was stillpending.

The EAGER-ENI-EMS Summer School onComputational Algebraic Geometry andApplications will be held in Eilat (Israel) on24-28 February 2002. The school includesan introduction on how to use computeralgebra systems such as SINGULAR andMACAULAY2 and packages such asSCHUBERT (intersection theory) forresearch in algebraic geometry and itsapplications. The programme consists oflectures and practical exercise sessions infront of a computer. (EAGER is theEuropean Algebraic Geometry Educationand Research, and ENI is the EmmyNoether Research Institute forMathematics at Bar-Ilan University andthe Minerva Foundation.)

The EMS Summer School on ComputationalAspects of Fluid Mechanics will be held on 8-19 July 2002, in Brasov (Romania).

Plans for Summer Schools in 2003-5were also considered, as was the possibilityof applying to the EU for funding for the2003 summer schools.

The 2002 EMS Lecturer will be ProfessorGianni Dal Maso of the InternationalSchool for Advanced Studies (SISSA) inTrieste (Italy).

It was agreed to add Antoine Bodin(Besançon) and Philippe Tilleuil (CREM)to the membership of the EMS EducationCommittee.

Michele Emmer was added to the mem-bership of the Committee for Raising PublicAwareness of Mathematics.

The Executive Committee decided to setup a General Meetings Committee, with LucLemaire in the Chair (EU); the othermembers would be Renzo Piccinini (sum-mer schools), Rolf Jeltsch, Jean-PierreBourguignon (DMF), Ana Bela Cruzeiro(SPM), Michael Sorensen (BernoulliSociety) and Mina Teicher (EMS ExecutiveCommittee). Among other ideas, thecommittee should discuss EU 6thFramework Programme funding for EMSmeetings, and the possibility that the EMShold regional meetings with member soci-eties.

Berlingen DeclarationSebastia Xambo had written an interestingreport on the Berlingen meeting for theJune EMS Newsletter. In short, the decla-ration is as follows:1.The presence of applied mathematics in

EMS bodies and policy decision makingshould be significantly increased.

2.The EMS Applied MathematicsCommittee must be kept an active bodyfor the time being. Its mission statementshould be adapted to the new role of thecommittee. Its Chair should be invitedto the Executive Committee meetings.

3.Pure and applied mathematics shouldbe equitably represented in the publica-tions of the EMS.

4.Special interest groups should be creat-ed gradually inside EMS.

5.The EMS should consider increasing itsactivities by collaborating with interna-tional, national and regional societies inorganising meetings.

6.The EMS should further develop itsSummer School Programme, and shouldcontinue to include topics in both pureand applied mathematics.

7.The EMS should work towards the goalsthat(a) students majoring in mathematics

should be exposed to applications ofmathematics in the sciences or inother areas;

(b) high-school teachers should haveadequate education in applied math-ematics and mathematical model-ling.

8.The EMS should formulate a positionwith regard to the Bologna declarationof 1999.

9.The EMS should continue to raise pub-lic awareness of mathematics; the EMSshould promote local initiatives, encour-age collaboration with various organisa-tions, and collect and disseminate infor-mation on initiatives of member soci-eties in this area.

The declaration was accepted as a positivestatement, which the EC will endeavour tofollow, looking at practical methods ofimplementation. The BerlingenDeclaration will be an item on the agendaof the 2002 Council meeting. It was alsoagreed that the President should ask theApplied Mathematics Committee toencourage nomination of a reasonablenumber of applied mathematicians asCouncil delegates.

Relations with MathematicalInstitutions/OrganisationsPeter Deuflhard reported that about 500participants (including 42 speakers) had

registered for the Berlin EMS-SIAM confer-ence in September 2001. The meeting con-sisted of 10 invited lectures, 151 talks, 37mini-symposia and one Round Table, aswell as posters. Benoit Mandelbrot wouldgive a lecture by TV from the USA.Funding had been received from the EU,the German Science Fund and the EMS,and an application to UNESCO was stillpending; the sponsors of the meeting alsoincluded Springer-Verlag. The moderatorfor the Round Table on AppliedMathematics would be Martin Grötschel.There was an interesting discussion on thepossibility of future joint meetings withSIAM and other bodies.

EMS NEWS

EMS December 20016

Tony Gardiner

Peter Deuflhard

Olli Martio had been elected as an EMSrepresentative on the Board of the BanachCentre for the Mathematical Sciences for 2001-4. It was agreed to re-elect Marta Sanz-Sole to a second term (2002-5) and to electRolf Jeltsch to a first term on the Board(2002-5).

It was agreed that the EMS shouldbecome a member of CIMPA (CentreInternational de Mathématiques Pures etAppliquées).

Stockholm European Congress ofMathematicians (4ECM) in 2004The dates for the Congress will be 27 June- 2 July 2004. A Letter of Understandingbetween the Organising Committee and

the EMS was agreed, subject to minormodifications.

The composition of the OrganisingCommittee of the 4ECM was agreed as: AriLaptev (President), Anders Lindquist,Christer Kiselman, Torsten Ekedahl,Mikael Passare, Ulf Persson and Kjell-OveWidman. A preliminary list of members ofthe Scientific Committee was also discussed;Lennart Carleson (Stockholm) will chairthe committee, and the deputy chair willbe Bjorn Engquist.

The Executive Committee discussedpossible names to chair the Prize Committee.It was suggested that at least one memberof the EMS Executive Committee shouldserve on the Prize Committee, to avoidproblems developing. Nominations forprize-winners from the mathematical com-munity would be sought. The point wasmade that nominees should not benefitfrom multiple nominations, in order toavoid influence from pressure groups; theonly criterion that mattered should be themerit of the proposed person. Work wascontinuing on the guidelines for the PrizeCommittee; the 2002 meeting of the EMSCouncil will decide on the final guidelines.It was however agreed that the age limitfor prize-winners should be 34 years, plusa further 3 years in the case of a brokencareer.

A preliminary budget for the 4ECM wasdiscussed; this incorporated a reduced feefor early registration and a significantreduction for EMS individual members. Itwas agreed to approach UNESCO andmember societies of the EMS for funds tosupport participation by EasternEuropean mathematicians.

In the run-up to the 4ECM, it was

agreed to hold an Executive Committeemeeting in Stockholm in September 2002.European Congress of Mathematicians in2008: Information for Possible ApplicantsA call for outline bids for the 5ECM will bepublished on EMIS and in the EMSNewsletter, with a deadline of 31 December2002; if there are at least two bids, fullerbids will be requested by 30 June 2003. Inthe summer of 2003 a site committee will beformed, to be followed by a recommenda-tion to the Executive Committee in theautumn of 2003. The EMS Council willmake the final decision in 2004, immediate-ly before the 4ECM.

Membership mattersIt was agreed to recommend to Council theraising of class of the Israel MathematicalUnion from Class 2 to Class 3.

Society elections in 2002The Executive Committee discussed possi-ble names for its nomination for officerposts and Executive Committee member-ship for the period 2003-6.

EMS budgetary mattersIt was agreed to propose to Council in 2002that the corporate fee be raised from 340 to360 euro.

Changes to the EMS Statutes and By-lawsWork had continued on possible changes tothe Statutes and By-laws, to clarify andimprove their operation. The ExecutiveCommittee discussed a draft, and agreed tolook again at a revised draft in February2002. It was agreed to propose to Councilthat academic institutions as institutionalmembers should have a new fee category ofx (Rule 25), and that other institutionalmembers should continue to pay an annualfee of 3x.

Bologna DeclarationVery little response had followed from theeditorial on the Bologna declaration in theJune Newsletter or from member societies.This surprised the Executive Committee!

PublicationsThe subscription price for the Journal of theEMS (JEMS) had remained constant untilnow, and needed to be reviewed. TheExecutive Committee accepted 210 euro asa basic price for the 2002 subscription toJEMS. The Publications Officer agreed tocheck with Springer on any additional sub-scriptions via the LINK scheme; and to urgeSpringer to include a credit card paymentoption on its subscription renewal form.

The distribution of the EMS Newsletter isaround 2500 copies of each issue. TheExecutive Committee discussed the level ofrevenue from advertising in the Newsletter.The Societys General Purposes Committeehad agreed to increase the Newslettersadvertising rates from 1 January 2002 byaround 6% over the figures that appliedfrom 1999 to 2001, and to encourage morejob advertisements in the Newsletter, as thecost to advertisers of around £100 is verycheap. The General Purposes Committeehad also agreed to increase the 2001 com-

mercial annual subscription price tolibraries and departments of the Newsletterof 60 euro to 65 euro in 2002. Discussionswould be held shortly in relation to review-ing the prices of inserted material in theNewsletter mailings.

The Publications Officer, CarlesCasacuberta, tabled the list of EMS books inthe Springer series: N. J. Cutland: Loeb Measures in Practice:

Recent Advances, Lecture Notes in Math.1751 (EMS Sub-series), Springer-Verlag,Berlin-Heidelberg, 2000 (1997 EMSLectures)

Diaz (ed.): Mathematics and Environment(2nd Diderot Mathematical Forum, 1997)plus a substantial list in preparation.

Future meetings of the ExecutiveCommitteeThe following indicative dates and locationsfor future meetings were agreed: Spring 2002 in Brussels (Belgium), on 9-

10 February; Summer 2002 in Oslo (Norway), on 31

May 2002 (before the Council meeting); Autumn 2002 in Stockholm (Sweden).

David A. Brannan

EMS NEWS

EMS December 2001 7

A commonsense tip

From time to time, active mathemati-cians receive invitations to submitpapers to research journals or confer-ences, to have their name included asa member of a journal editorialboard, to speak at a conference, toparticipate in a conference, to havetheir name included as a member ofthe organising committee of a confer-ence, and so on. Sometimes theseinvitations include a request for pay-ment of some sort (e.g. conferencefees, page charges, or whatever).

The vast majority of such invitationsare of course entirely genuine andwelcome to the recipient! However, asmall minority of such invitationsrepresent money-making schemes ofa type that might not be immediatelyobvious to the recipients, and thatmight not be at all welcome to them ifthey understood what was going on.The internet is often used for suchinvitations, just as it is for a numberof other doubtful financial schemes.

If you receive an invitation to beinvolved in a journal or conferencewhose organisers reputability you donot already know, it is wise to checkout the integrity of what is proposedbefore agreeing to let your name beused and before sending any money.

David A. Brannan

Renzo Piccinni

The following nominations for the EMSCouncil were received by the deadline, 15November. As there were fewer nominationsthan vacancies, the following four persons havebeen elected delegates of individual members forthe years 2002-05.

Marina Marchisio Torino (Italy), e-mail:marchisio@dm.unito.itProposer: Alberto Conte; seconder: GiuseppeAnichiniBiography: I was born in Boves (Italy) on20/12/1969. I studied at the University ofTorino, where I got my Doctorate inMathematics in March 1999 for a Thesison Unirational quartic hypersurfaces, underthe scientific supervision of Alberto Conte.Since July 1999 I have been a Researcher(Ricercatore) in the Faculty of Sciences ofthe University of Torino. My researchfield is algebraic geometry in particular,rationality problems for higher-dimen-sional algebraic varieties. Since 1996 Ihave been acting as editorial secretary ofthe Bollettino dellUnione MatematicaItaliana. I have been a member of theCouncil of the European MathematicalSociety for 1998-2001 as a representativeof individual members.Statement: If I am re-elected, I shall contin-ue my action of the previous four years infavour of European Young Researchers, inorder to get more jobs for them in the uni-versities and research institutions.

Vitali Milman, Tel Aviv (Israel); e-mail:milman@post.tau.ac.ilProposer: Dan Haran; seconder: ZeevRudnick.Biography: Professor at Tel-Aviv University,1973-. Incumbent, Argentinia Chair inMathematics, Tel-Aviv University. Born:1939. Education: Ph.D. 1965, Institute forLow Temperature Physics, Kharkov; D.Sc.1970, Institute for Low TemperaturePhysics, Kharkov. Fields of specialisation:Functional analysis; convexity; asymptoticgeometric analysis. Publications: over 130papers and 11 edited books. Invitedaddresses: ICM1986, Berkeley (analysis sec-tion); ICM1998, Berlin (analysis section);ECM1996, Budapest (plenary address);and over 150 colloquia and seminar lec-tures at major universities and talks atinternational conferences. Editor of GAFA(Geometric Analysis and Functional Analysis);member of Editorial Board of Israel J.Math. President, Israel Math. Union(2000-); Member, Board of Governors ofTel Aviv University (2001-); Member,Board of Directors, Weizmann ScientificPress of Israel (1983-92); Member, Boardof Directors, Institute of IndustrialMathematics, Beer Sheva (1992-95).Statement: I view the EMS as potentially themost important body representing andlobbying for mathematics in Europe. In

the current era of a united Europe, scien-tific funding increasingly depends on thedecisions of a supranational bureaucracythat is not easily accessible via nationalsocieties.

Maintaining and enlarging support formathematics within Europe requires vigor-ous lobbying efforts on the part of a bodythat can speak clearly and forcefully for theEuropean mathematical community as awhole. The only credible candidate forthis important role is the EMS. It alreadyproved its leadership, which I would like tosee broadened and strengthened.

On the world level, I see the EMS as pro-viding a useful and healthy balance toother groups within the InternationalMathematical Union which can serve tofurther the interests of European mathe-matics and mathematicians within thatbody.

Finally, as a professional society, theEMS must continue and expand its activi-ties in organising European Math.Congresses, in support of joint Europeanmathematical conferences, scientificexchange, and the easy movement ofmathematicians between the countries ofEurope.

Robin Wilson, Milton Keynes (UK), e-mail:r.j.wilson@open.ac.uk

Proposer: David Brannan; seconder: BarbaraMaenhaut.Biography: I am a senior lecturer in thepure mathematics department of the OpenUniversity, UK, as well as being a Fellow ofKeble College, Oxford University. I amcurrently Visiting Professor in the Historyof Mathematics at Gresham College,London, and have also held a number ofvisiting appointments in the USA.

My two main research areas are in graphtheory/combinatorics and the history ofmathematics, and I have written and edit-

ed about 25 books in these subjects, as wellas a substantial number of research andexpository papers. I am a great believer inthe propagation and popularisation ofmathematics, and try to achieve thisthrough my books and in the 30-40 popu-lar lectures I give each year to various audi-ences.

Over the past three years, I have beenheavily involved with the activities of theEuropean Mathematical Society, as Editor-in-Chief of the EMS Newsletter, as a fre-quent attender of Executive Committeemeetings, and as an invited speaker at thefourth Diderot mathematical forum. Statement: For the past three years I havebeen Editor-in-Chief of the EMS Newsletter,a role I hope to continue for some time tocome. I am running for the EMS Councilbecause I wish to become more closelyinvolved with the activities of the Society,and because I believe that my knowledgeof recent EMS events, acquired throughworking on the Newsletter, could be of valueto the Council.

Sebastià Xambó-Descamps, Barcelona(Spain); e-mail: sebastia.xambo@upc.es

Proposer: Manuel Castellet; seconder: CarlesCasacubertaBiography: Full Professor of Informationand Coding Theories at the TechnologicalUniversity of Catalonia (UniversitatPolitècnica de Catalunya) since 1993, andVice-Rector of Information andDocumentation Systems April 1998-March2002. My main research interests at present arein the applications of algebraic geometryto fields such as enumerative geometry,error-correcting codes, computationalmathematics and mathematical physics.Recently I coordinated the development ofWIRIS (TM), a multilingual, web-accessiblesystem, to cover a wide range of computa-tional mathematics needs (which has beeninstalled by the Catalan Ministry ofEducation to meet the computationalneeds of students and teachers of primaryand secondary schools and includes facili-ties for the production of digital teachingand learning materials).

Born in 1945, married with two

EMS NEWS

EMS December 20018

EMS Council electionsEMS Council elections

daughters, and first lecturer in theUniversity of Barcelona since 1969, I spentthe terms 1977-78 and 1978-79 at theUniversity of Brandeis (Massachussetts,USA), where I learned algebraic geometryfrom Teruishi Matsusaka, David Eisenbudand Michael Harris. After receiving aMaster of Arts in Mathematics in 1978, Iobtained my PhD in Barcelona in 1991. Iwas associate professor of geometry andtopology in the University of Barcelona1982-89 and full professor of algebra inthe Universidad Complutense of Madrid1989-93.Statement: President of the CatalanMathematical Society, of the Institute ofCatalan Studies, since February 1995 (andleaving office not later than December2002); I was the president of the Executiveand Organising Committees of the 3rdEuropean Congress of Mathematics inBarcelona, 10-14 July 2000. My motivationfor such undertakings as these, stems fromthe desire to contribute in as an effectiveway as possible to the development of areally comprehensive European space formathematics where everybody can deliverthe best of themselves.

The full list of delegates of individual mem-bers for 2002-03 is as follows:Giuseppe Anichini (1996-99-03), Dipto diMatematica Appl., G. Sansone, Via S.Marta 3, I-50139 Firenze, ItalyVasile Berinde (2000-03), Department ofMathematics, Univ. of Baia Mare, Victoriei76, RO-4800 Baia Mare, RomaniaGiorgio Bolondi (1996-99-03),Dipartimento di Matematica-Politecnico,Piazza Leonardo 32, I-20133 Milano, ItalyAlberto Conte (2000-03), Corso Francia,17, IT-10138 Torino, ItalyC. T. J. Dodson (2000-03), Department ofMathematics, UMIST, PO Box 88,Manchester M60 1QD, UKJean-Pierre Françoise (2000-03), Dept.Math., Univ. Paris 6, 4 Place Jussieu, Case172, F-75252 Paris Cedex 05, FranceSalvador S. Gomis (2000-03), DeptoAnalisis Matematico/Mat. Aplicada,Universidad de Alicante, Campus de SanVicente, ES-03080 Alicante, SpainLaurent Guillopé (2000-03), Dép. Math.,Fac. Sciences & Techniques, Université deNantes, 2 rue de la Houssinière, BP 92208,F-44322 Nantes Cedex 03, FranceKlaus Habetha (1996-99-03), Rektor,RWTH Aachen, D-52056 Aachen,GermanyWilli Jäger (2000-03), Inst. fürAngewandte Math., UniversitätHeidelberg, Im Neuenheimer Feld 294, D-69120 Heidelberg, GermanyTapani Kuusalo (1996-99-03),Department of Mathematics, University ofJyväskylä, P.O. Box 35 (MaD), FI-40351Jyväskylä, FinlandMarina R. Marchisio (1998-01-05), ViaPrimula 20, I-12012 Boves (CN), ItalyLászló Márki (1996-99-03), MathematicalInstitute, Hungarian Academy of Sciences,Pf. 127, H-1364 Budapest, HungaryVitali Milman (1998-01-05), School ofMathematics, Tel-Aviv University, Ramat-Aviv, Israel

Andrzej Pelczar (2000-03), Institute ofMathematics, Jagiellonian University,Reymonta 4, PL-30-059 Kraków, PolandZéev Rudnick (2000-03), School ofMathematical Sciences, Tel AvivUniversity, Ramat Aviv 69978, IsraelGérard Tronel (2000-03), Labo dAnalyseNumer., Univ. P. et M. Curie, 4 pl. Jussieu,

F-75252 Paris Cedex 05, FranceRobin Wilson (2002-05), Department ofPure Mathematics, The Open University,Milton Keynes MK7 6AA, United KingdomSebastià Xambó-Descamps (2002-05),Department of Mathematics Apl. II,Technical University of Catalonia, ES-08028 Barcelona, Spain

EMS NEWS

EMS December 2001 9

EAGER - ENI - EMS

Summer School,

Eilat, Israel

24th-28th February 2002The SUMMER SCHOOL is an introduction to the use of computer algebra systems, such asSINGULAR and MACAULAY2, and packages, such as SCHUBERT (intersection theory), forresearch in Algebraic Geometry and applications. The programme consists of lecturesand practical exercise sessions on the computer. The topics to be considered include:computer algebra systems, Groebner bases and syzygies, ideal and radical member-ship, manipulating ideals and modules, Hilbert polynomials and Hilbert functions, elimi-nation, computations in local rings and Milnor numbers, homological algebra (construc-tive module theory, Ext and Tor, sheaf cohomology, Beilinson monads), primary decom-position, normalization, rings of invariants, parametrization, deformations, intersectiontheory, applications to special varieties, computer vision, and coding theory.

Course Director: Prof. Wolfram Decker (Saarbrücken, Germany). Guest lecturer: Dr. Jeremy Kaminski (Bar-Ilan, Israel).

Participants will need to bring laptops. The level will be appropriate for graduate stu-dents. There will be limited financial support for local expenses.

Organisers: Prof. Mina Teicher and Prof. Boris Kunyavski of the Emmy Noether Institute.(Conference Secretary: Ms Chen Fireman) email: eni@macs.biu.ac.il

http://www.cs.biu.ac.il/~eni/ann1-2002.html

ComputationalAlgebraic Geometry

and Applications

AustraliaUrbas, John

BelgiumBair, JacquesBellemans, J.Borrey, SabineBotterman, StefaanDe Maesschalck, P.Dehaye, Paul OlivierDevillers, AliceFiorini, SamuelGeivaerts, MarcelKuijken, ElisabethLuyckx, DeirdreStulens, KoenMielants, WimQuarta, LucasRigo, MichelRoisin, Jean-RogerPlastria, FrankSebille, MichelSimar, LéopoldStienon, MathieuStulens, KoenTeugels, JefToint, PhilippeVan Camp, EllenWarrinnier, AlfredZhang, Yinhuo

BrazilBarbosa, RommelFerreira, Jorge

CanadaFillmore, PeterLakhany, A.Thomas, R. S. D.

Czech RepublicEphremidze, Lasha

CroatiaIvansic, Ivan

DenmarkBennedsen, HelgeBooss, BernhelmBrons, MortenCarstensen, AngelaChristiansen, EdmundClaudius, MichaelConradsen, KnudHaugaard, KristianHoffmann-Jorgensen, JorgenHogsbro-Thygesen, UffeKiming, IanKjargaard Pedersen, GertKjeldsen, TinneLynggaard, JoergenMadsen, TomSinclair, RobertSkovsmose, OleSørensen, MichaelThusgaard Ruhoff, Peder

FranceBoivin, DanielBodin, AntoineBorrelli, VincentCerf, JeanChavent, GuyChéniot, DenisCont, RamaCoupet, BernardDuval, YvesElskens, YvesJambu, MichelMardin, Arif

Periaux, JacquesRhin, GeorgesRoos, GuyTimmel, Jean-FrancoisTrotman, DavidUrsat, XavierVergne, MicheleWaldschmidt, Michel

GermanyAlefeld, Götz E.Cleve, LudgerFrommer, AndreasFuegenschuh, ArminHaase, PeggyHeinlein, PeterHolzleitner, LudwigHubski, MarthaKawohl, BernhardNakamura, Shu GilbertSmoczyk, KnutWerner, Dirk

GreeceDassios, GeorgeMavridis, N.Vlamos, Panayiotis

GuatemalaMoreira Galicia, Manuel

Hong KongHu, K. Y.

IrelandHutchinson, Kevin

IsraelAbarbanel, SaulAdin, RonAgranovsky, MarkAlesker, SemyonAlkalai, NuritAmram, MeiravArad, ZviBeck, JonathanBercovier, MichelBerezina, MiriamBesser, AmnonChillag, DavidCwikel, MichaelDax, AchiyaDula, GioraElin, MarkEnden, GioraFarber, MichaelGelaki, ShlomoGilat, DavidGitik, MotiGohberg, IsraelGordon, YehoramHaran, DanHorwitz, Lawrence PaulJuhasz, AryeKrasnov, YakovKaminski, Jeremy YermiyahuKaplan, GilKarp, LaviKheifets, AlexanderKrushkal, SamuelLawrence, RuthLeborgne, DanielLeizarowitz, ArieLerer, Leonid (Arie)Levy, AzrielLevy, EliahuMargolis, Stuart W.Megrelishvili, JonathanMerzbach, EliMoran, Gadi

Novick-Cohen, AmyOlevskii, AlexanderReisner, ShlomoRoitman, MosheRom-Kedar, VeredRosset, ShmuelSchuss, ZeevSever, MichaelShoikhet, DavidShustin, EugeniiShvartsman, LudmilaSodin, MikhailSrebro, UriTkachenko, VadimTsirelson, BorisWeir, YitzhakWeiss, Benjamin

ItalyBalossini, MarioCapalbo, AntonioCasiraghi, SergioCesarano, ClementeChiaretti, MauroCichero, AnnaCipollone, RobertoCitrini, ClaudioConti, DavidDi Lorenzo, EmiliaEschgfaeller, JosefFiorito, GiovanniFuri, MassimoFurnari, GiuseppeGaeta, G.Gonella, CorradoGori, FrancoMachi, AntonioMicelli, GiuseppeMoscucci, ManuelaPaveri Fontana, StefanoPennisi, MarioPizzimenti, Pasquale FrancescoPuccio, LuigiaRivara, LuigiRomito, MarcoRuf, BernhardSalvetti, MarioSavare, GiuseppeSibillo, MarilenaSmit Ghinelli, DinaVolcic, AljosaZanchetta, Nadir

LuxembourgBausch, Raymond

NorwayReichelt, Yngvar

PolandCiesielski, KrzysztofCzerwinska-Lenkowska, TeresaPisarek, JerzyRadzikowska, EugeniaRogula, DominikSztyren, Malgorzata

PortugalGuerreiro, Antonio A.Pereira, Antonio M. R.Santos, Carlos A.

RomaniaRadulescu, Vicentiu

RussiaYagola, Anatoly

South AfricaKalinde, Albert

South KoreaKim, A. C.

SpainArias Cano, CristinaBonilla, Luis L.Cal Casals, Fernando

Carro Rosell, Maria JesusCerda i Martin, JoanCifuentes Muniz, PatricioCurto Dias, JosepFernandez Garcia, GuillermoGalindo Pastor, CarlosGiraldo Carbajo, AntonioGomez Torrecillas, JoseHernandez Penalver, GregorioLopez Gonzalez, Luis MariaMartin del Rey, AngelMartinez Pastor, AnaOjeda Aciego, ManuelOrtega Titos, MiguelPadron Fernandez, EdithPedregal Tercero, PabloPerez Riera, MarioPison Casares, PilarRichard, Philippe R.Romance del Rio, MiguelSanchis Lopez, ManuelSastre Rosa, Maria AsuncionSoria de Diego, Javier

SwedenAndersson, Karl Gustavde Gosson, M.Essén, MattsHansson, ÖrjanPassare, MikaelPefferly Jr, R. J.

SwitzerlandBissegger, ElenaBuchmann, Fabian MartinFrauenfelder, PhilippImhof, Jean-PierreIozzi, AlessandraIshikawa, MasaharuJainz, MichaelJoosten, RobertKuensch, Hans RudolfLoher, DamianMatache, Ana-MariaMotamen, SiminOrtega, Juan PabloReimann, H. M.Savelieva, MarinaSchmidlin, GregorStruwe, M.Todor, Radu-AlexandruTorrilhon, ManuelToselli, AndreaTroxler, AndreasWihler, ThomasZimmermann, Susanne

TurkeyAkinci, Karen

United KingdomByott, NigelDeitmar, AntonGardiner, A. D.Hasson, R.Jarvis, T. M.Keeling, H.Lillington, John NewmanPantilie, R.Rubidge, N. W.Stewart, J.Wiltshire, RonaldWilson, P. L.Wotherspoon, Craig Iain

United StatesEdwards, Robert D.Linnell, P. A.Martens, JohanNorton, JuliaNworah, Kingsley I.Saloff Coste, Laurent

UkraineSuvorov, Serghey G.

UzbekistanAripov, Mersaid

EMS NEWS

EMS December 200110

New EMS membersWe welcome the following new individual members to the

European Mathematical Society.

EurEuropean Congropean Congress of Mathematicsess of MathematicsCall for Bids for the 5ECM

Outline bids from possible organisers of the 2008 Congress are now invited, and should reach the EMS Secretariat by 31December 2002. The address of the Secretariat is Mrs Tuulikki Mäkeläinen, Department of Mathematics, University ofHelsinki, P.O. Box 4, FI-00014 Helsinki, Finland (Tel: +358-9-1912-2883; Fax: +358-9-1912-3213; e-mail: tuulikki.make-lainen@helsinki.fi).

The information below may be helpful to possible organisers. Informal discussions are welcomed, and may be addressed tothe Secretary David Brannan (e-mail: d.a.brannan@open.ac.uk) or any other member of the Executive Committee.

General information on ECMsEuropean Congresses of Mathematics are organised every four years. The first Congress was held in Paris in 1992, the secondin Budapest in 1996, and the third in Barcelona in 2000. In 2004 the Congress will be held in Stockholm. The next free slotfor a Congress is the year 2008. The Congress must be in Europe.

Experience of previous Congresses suggests that the attendance might be expected to be around 1000 mathematicians. Theduration has so far been 5 days. 10 EMS Prizes are awarded to young outstanding European mathematicians at the openingceremony.

The Congress programme should aim to present various new aspects of pure and applied mathematics to a wide audience,to offer a forum for discussion of the relationship between mathematics and society in Europe, and to enhance cooperationamong mathematicians from all European countries. The standard format of previous ECMs has been:- about 10 plenary lectures;- section lectures for a more specialised audience, normally with several held simultaneously;- mini-symposia;- film and mathematical software sessions;- poster sessions;- round tables.

An exhibition space for mathematical societies, booksellers, etc. is required. No official language is specified and no inter-pretation is needed.

The Proceedings of the previous ECMs have been published by Birkhäuser-Verlag.

Decision process for 5ECM(i) Bids are invited via this notice in the EMS Newsletter in 2001, and via letters to the EMS member societies sent out in 2001

by the EMS Secretariat; the deadline for bids is 31 December 2002. These bids need only be outline bids giving a clear ideaof the proposal and possible sources of financial and local support.

(ii) Early in 2003 the Executive Committee of the EMS ('EC') will consider the bids received. It will invite one or more of thebids to be set out in greater detail so that it can decide which bids are sufficiently serious options to be considered further.The deadline for such 'worked up' bids is 30 June 2003.

(iii)The EC will then create a short-list of sites that appear to offer the best possibilities for a successful Congress.(iv) The EC will then appoint a Site Committee to visit the short-listed sites between July and December 2003 to check a range

of items in connection with the development of the Congress. For example:- Size and number of auditoriums; location and equipment- Room for exhibitors- Hotel rooms and dormitories; location, prices, number in different categories and transportation to lectures- Restaurants close to Congress site, number and prices- Accessibility and cost of travel from various parts of Europe- Financing of the Congress; support to participants from less favoured countries, in particular- Financing for the EMS Prizes- Experience in organising large conferences- Timing of the Congress- Social events- Plans to make publicity for Mathematics on the occasion of the Congress

(v) In 2004 the EC will make a recommendation for the site to the EMS Council on the basis of the bid documents and the SiteCommittee report. The Council will reach its decision prior to 4ECM in 2004.

Relations between the EC and the Organising Committee of 5ECMAfter the Council decision, the local organisers will be asked to present a draft budget and an outline of the programme of theCongress. The actual Congress organisation is the responsibility of the local organisers.

At least two committees must be appointed - namely, the Scientific Committee and the Prize Committee. The ScientificCommittee is charged with the responsibility for conceiving the scientific programme and selecting the speakers. The PrizeCommittee is charged with the responsibility of nominating the EMS Prizewinners.

For each of these committees the Chairs are suggested by the local organisers and agreed after consultation with the EC. Inturn, the members of the committees are suggested by the Chairs, and are approved after consultation with the EC.

The local organisers are responsible for seeking financial support for the Congress and for the meetings of its committees.However the EMS commit to provide some financial support for the travel of Eastern European mathematicians to the ECM,and would also assist and advice in seeking sources of funds, in particular from the EU. The EMS and the local organisersshould be partners in the effort to find funding support for the prizes.

The level of the registration fees is of great importance to the success of an ECM. The EC asks that it should be involvedbefore a final decision on the level of fees is made; members of the EMS normally receive a reduction of some 20% on the reg-istration fees.

The EC would wish to be informed of progress at its regular meetings. The EC would be pleased to offer advice to the localorganisers on matters such as the scientific programme, budgetary developments, registration, accommodation, publications,web site, etc. Publicity for the ECM via the EMS Newsletter and the EMIS site is strongly recommended.

Marta Sanz-Solé and David Brannan

EMS NEWS

EMS December 2001 11

Fermats outwardly uneventful life is soon told.André Weil [13]

The 400th birthday of Pierre de Fermat,the great seventeenth-century Frenchmathematician, was celebrated in 2001.However, this is probably based on afallacy (see [2]): Fermat was probably bornin 1607, or in the first days of January1608, in Beaumont-de-Lomagne. He wasthe son of the rich wholesaler andmanufacturer Dominique Fermat, and hismother, Claire De Long, his fatherssecond wife, came from a noble family ofjurists (see [11]). Thus, strictly speaking,the celebrations and conferences withrespect to Fermats 400th birthday arepremature. But we wont spoil the fun -well join the celebrations of Fermatsbirthday, and report on his little-knownprivate and professional life.

In the second half of the fifteenthcentury, the Fermat family apparentlyemigrated from Catalonia to Beaumont-de-Lomagne, a fortified village with amarket, about 55 kilometers to the north-west of Toulouse. There, in the sixteenthcentury, Pierre Fermats grandfatherAnthoine run an ironmongery that earnedhim a modest fortune which hebequeathed to his two sons Dominique(from his first marriage, Fermats father)and Pierre (from his third marriage,Fermats godfather). Both sons increasedtheir fathers inheritance to the best oftheir abilities. Dominique was particularlysuccessful. A merchant who ran a leatherwholesale trade with Italy, Spain andEngland, he also had a flourishing limefactory and gained considerableprosperity. He invested his profits innumerous farms and other plots of land,which he leased on the basis of metayagecontracts.

Through his marriage with anoblewoman, Claire de Long, reflectinghis increased standing, he gained accessfor his sons Pierre and Clément to thenoblesse de robe. His familys socialpromotion was planned well in advance:for, the only way to achieve it was to buythe office of a parliamentary councillor(conseiller) at one of the Supreme Courts ofJustice (cours de parlement) in the Frenchprovinces, just as in Toulouse orBordeaux. This custom, already disputedduring the Ancient Régime but completelylegal, had been introduced by the FrenchCrown in the sixteenth century because oflack of money. The prerequisite for thiswas not only a respectable fortune. Onehad also to gain appropriate qualifications:three years of study of law, leading to abaccalaureus (juris civilis), and four years ofpractical experience as a lawyer at one ofthe Supreme Courts. Further, a suitable

office had to be up for sale, and thesupport of members of the particularparliament was needed, requiringsubstantial favouritism. At the end therewould be an entrance examination in lawwhich not everyone passed.

Pierre de Fermat spent his schooldayswith the Frères Mineurs Cordeliers in hishome town. These were Franciscans whohad settled in Beaumont around 1515 andfounded a demanding grammar school inwhich classical Greek was taught, inaddition to Latin, Italian and Catalan.This was unusual for the time in a smallplace with only 3000 inhabitants. ForPierre, who left school in 1623 at the age of16, his good command of classicallanguages was a crucial precondition forhis study in Orléans.

His choice of this place for study was wellfounded. The town on the Loire had anold and famous faculty of civil law whose

reputation far beyond France attractedstudents from all parts of Europe - aboveall from Scotland, the Netherlands andSwitzerland, as well as from Germancountries where students of Lutherandenomination formed a high proportion.In the sixteenth century Orléans had madea name for itself as a stronghold ofhumanistic jurisprudence. In this, acritical-philological return to the classicalorigins and sources of Roman law(particularly Justinian) played a centralpart. A reliable mastery of Latin andclassical Greek was indispensable for thesestudies, and the classical languages wereespecially cultivated by the faculty of theartes liberales of Orléans. A baccalaureatefrom Orléans undoubtedly gained a youngjurist a considerable reputation.

Around August 1626, Pierre de Fermatpassed his examinations in Orléans, andduly received his certificate for successfully

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EMS December 200112

PPierrierre de Fe de Fermat (1601? - 1665)ermat (1601? - 1665)His life beside mathematics

Klaus Barner

Fermat Memorial with the sculpture by Falguière in front of the covered market ofBeaumont

passing the examination of baccalaureusjuris civilis. In the following monthDominique Fermat wrote his last will andtestament. Giving a compensation to hisyounger son Clément, and fixing thedowries of his daughters Louise and Marie,he chose his elder son Pierre as sole heir.

Pierre Fermat proceeded to Bordeauxand was sworn in as a lawyer by the GrandChambre of the parlement de Bordeaux inOctober 1626. Being called to the Bar ofone of the French provincial parliaments,he had to set up in practice as a lawyer,because this was by royal law aprecondition for recognition as a conseillerby the Minister of Justice. After his naturalchoice of Orléans as a place of study, hisselection of Bordeaux for practising as alawyer was surprising; for many differentreasons Toulouse was a more obviouschoice. It is likely that Fermats choice ofBordeaux is connected with hismathematical leanings.

In Bordeaux, there was a small circle oflovers of mathematics, of whom the namesDEspagnet, Philon and Prades are knownfrom Fermats correspondence; ÉtienneDEspagnet, whose father had been firstpresident of the parliament of Bordeauxand a friend of Viète, owned Viètes workswhich were very difficult to obtain at thattime. Here Fermat, who was just 20,started his mathematical career. But whoadvised him to settle as a lawyer inBordeaux? It was probably JeanBeaugrand, who cultivated scientificrelations with the gentlemen in Bordeaux.Fermat may have made his acquaintance inAugust 1626 in Orléans. At any rate, it issignificant that Beaugrand followedFermats mathematical career withparticular interest, and he always proudlyreported on Fermats achievements duringhis journeys to Italy and elsewhere.Beaugrand obviously felt that he haddiscovered Fermat.

When Dominique Fermat died on 20June 1628, Pierre became a wealthy man,and had only another two years to spend asan avocat in Bordeaux. If the opportunitythen arose for him to buy a conseillers office(in Toulouse, preferably), the first stage ofthe family plan would be achieved. Thisopportunity arose at the end of 1630,during a severe plague epidemic thatcarried off numerous conseillers auparlement in Toulouse. On 29 December1630, Fermat concluded an advancecontract with Ysabeau de la Roche, widowof Pierre de Carrière, conseiller au parlementde Toulouse and commissaire aux requêtes,regarding the purchase of the deceasedsoffice.

The purchase price of 43500 livres, withan initial payment of 3000 livres on takingup the office, represented a usual, butenormous, sum. A farmer could earnabout 100 livres per year, a parish priestsome 300 livres, and a busy conseiller up to1500 livres on which he then had to paytax. From an economic point of view sucha purchase was a miserable deal,particularly since by royal law the conseillerswere not allowed to carry on a trade orpractise a craft; nearly all of them earned

their living from their estates, which theyleased. Fermat, who had inherited fromhis father six farms and numerous otherpastures, gardens and vineyards, was noexception in this respect. Only verywealthy landowners could afford theluxury of purchasing an office of that kind.The profit consisted of the advancementinto the noblesse de robe, the socialreputation and privileges that went with it,and the participation into political power.

After Fermat had asked for the kingsconsent and passed the prescribedentrance examination of the parlement deToulouse, he was sworn into office by theGrand Chambre on 14 May 1631. From thismoment onward, he enjoyed all the rightsand privileges of a conseillers office - theincome from his office, and the right to use

the title éculier and put de before hisname.

The close chronological linking betweenFermats appointment as conseiller auparlement and his marriage with Louyse deLong, the daughter of Clément de Long,conseiller au parlement de Toulouse, isinteresting. The marriage contract wasconcluded on 18 February 1631, and on 30March, de Long paid his future son-in-law2865 livres as a down payment on thepromised dowry of 12000 livres. Thechurch wedding took place on 1 June inthe Cathétrale St-Etienne of Toulouse.

The de Longs, remote relatives ofFermats mother, lived in Toulouse in therue Saint-Remesy, and also possessed ahouse in Beaumont-de-Lomagneadjoining the premises of the Fermatfamily. In that house Clément de Longused to spend his parliamentary vacations.Pierre and Louyse must have known eachother from childhood, and their marriageseems to have been settled by the familieslong ago, provided that Pierre made it toconseiller au parlement. Contemporariespraise the beauty, beguiling charm andcharity of the young woman who borePierre five children, Clément-Samuel,Jean, Claire, Catherine and Louise.

The French provincial parliaments ofthe Ancient Régime were not parliaments by

todays standards. The idea of separatingthe powers of legislature, executive andjudiciary, which had been elaborated byJohn Locke and Charles de Montesquieuand politically realised much later, was stillcompletely unknown in the seventeenthcentury. The parlements performed thetasks of law-making, administration andjurisdiction, so far as they had beentransmitted to them by the Crown for theprovinces administered by them.

The parliament de Toulouse was openedfor the first time in 1303. From the start,its area of responsibility included thecomplete south-east of the kingdom.Following the Parisian model, it had aGrand Chambre, the original chamber fromwhich all other chambers developed forprocedural reasons: the chambre criminelle(also known as la Tournelle) and twochambres des enquêtes. The Tournelle dealt inthe final instance with all offendersthreatened with corporal punishment, andno clergyman was allowed to be a memberof it; this chamber regularly delighted thecitizens of Toulouse with its publicexecutions. Each year two conseillers wereexchanged between the Grand Chambreand Tournelle, so that they were consideredas one chamber divided in two. In the twochambres des enquêtes civil actions weredecided in writing in the final instance.

The chairman of the Grand Chambre andhead of the whole parliament was thepremier président. He was the onlymagistrate who had not purchased hisoffice, being appointed by the king. Hisdeputies in the Grand Chambre were thechairmen of the other chambers and theprésidents à mortier (two or three perchamber) who had also bought theirprestigious offices, at three times the priceof the ordinary conseillers. They regularlyled the sittings of their chambers inrotation.

An ordinary conseiller, as Fermatremained all his life, could also play acentral role if he was appointed therapporteur of a case by the chamber.Additional income came with a rapporteursrole in a court case, and a hardworkingrapporteur could raise his incomesignificantly. Fermat was one of the mosthard-working rapporteurs of theparliament; for example, in a ten-weekperiod in the Tournelle from November1657 to January 1658, he wrote no fewerthan 34 rapports/arrêts. Fermat drew up hisfirst arrêt on 6 December 1632 in thechambre des requêtes, his first rapport in theGrand Chambre on 9 December 1654, andhis last arrêt in the chambre de lEdit on 9January 1665, three days before his death.

The four chambers mentioned aboveformed the proper cour of the parlement deToulouse. The chambre des requêtes in whichFermat took up his office of conseiller andcommissaire in 1631, did not belong to theproper cour of the parlement and was at thelower end of the parliaments hierarchy.Its members heard preliminary civil cases,leaving the final judgements to one of thechambres des enquêtes.

A commissariat aux requêtes was generally aposition for a beginner, allowing him to

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Two recent Fermat stamps

become acquainted with the practice of theparliament, but it gave no advancement.For this purpose, the conseiller had to sellhis office in the chambre des requêtes andpurchase an office in the proper cour of theparliament. Fermat duly gave up hiscommissariat des requêtes on 4 December1637, and acquired an office in the cour of

the deceased Pierre de Raynaldy. He wasregistered at the court of the parliamenton 16 January 1638, and held this officeuntil his death.

During Fermats time as a commissaireaux requêtes he made the acquaintance ofhis long-time friend Pierre de Carcavi, whoin 1632 became his colleague at theparlement de Toulouse. Carcavi moved toParis in 1636 and mediated for Fermatwith Marin Mersenne and his Parisiancircle. Fermats long-standingcorrespondence with these gentlemenstarted a few days after Carcavis arrival atParis and lasted (with an interruption)until shortly before his death. Fermatsfamous dispute with Descartes occurred atthe time of his move from the chambre desrequêtes to the first chambre des enquêtes.

The chambre de lEdit de Nantes belongedto the parlement de Toulouse. This chamberwas created in 1598 by Henri IV, withequal representation by members of theReformed Church and the RomanCatholic Church, and had its seat from1632 to 1670 in Castres, 75 kilometres tothe east of Toulouse. In this chamber, allcases of conflict, and all criminal cases inwhich adherents of both religions wereinvolved, were settled. It consisted of twopresidents, one from each Church, as wellas ten magistrates of each denomination.The judges, members of the ReformedChurch, were local and had purchasedtheir offices. Each year, eight of theCatholic judges were elected by the kingfrom a list of twelve conseillers au parlementde Toulouse that had been compiled by theGrand Chambre. On 29 May 1638, theGrand Chambre nominated Fermat for the

first time for the chambre de lEdit, andFermat was selected by the king on 16 July.He spent the session of 1638-9 with hisfamily in Castres.

From 1646, Fermats letters to hiserudite collegues became sparse, and forseveral years his mathematicalcorrrespondence almost stopped

completely. Why was this? Deterioratingmental ability? (Fermat was just forty yearsold.) Mersennes death on 1 September1648? (His place was soon taken over byCarcavi.) We have rather to look forreasons among the strains of Fermatsprofessional life; these were connectedwith social and political disturbances:peasants revolts in the south of Francearising from brutal methods of taxcollections, the rebellion of the Frondeagainst Mazarin, and the war againstSpain. At the beginning of the 1650s, thelast great French plague epidemic brokeout, followed by famine.

We are rightly used to seeing Fermat asthe great mathematician and humanistscholar. But according to his conceptionof himself, he was first and foremost ajudge. At the parliament of Toulouse hehad a seat for life. Even though he couldlive off his possessions in Beaumont-de-Lomagne, he regarded his job as conseillerau parlement de Toulouse as his proper lifeswork, and his career in this institution wasmore important to him than his reputationas a mathematician. Only when hisprofessional activities allowed him enoughleisure, such as when parliament was not insession during the numerous religiousfestivals, could he devote himself to hishobby of mathematics.

Fermat spent the great parliamentaryrecesses in September and October à lacampagne in Beaumont-de-Lomagne,where at harvest time he received his shareof the yields from the leased farms, asagreed by contract. He gave advice onlegal questions to the inhabitants of hishome town, and regularly took part in the

citizens meetings - his name turns up inthe minutes for many years - helping themwith particularly difficult items on theagenda. The Fermat family also showed itsclose attachment to Beaumont with charityand donations and by becominggodparents on numerous occasions. Veryoften Fermat had less time there for hisbeloved geometry than he had hoped.

The Huguenot stronghold Castres, seatof the chambre de lEdit de Nantes, was aparticularly strong attraction for Fermat.Again and again he tried, not alwayssuccessfully, to be proposed by the GrandChambre for the delegation to Castres andto be confirmed by the king. Between1632 and 1665, of the 45 conseillers auparlement de Toulouse delegated to Castreswhose term was renewed by the king for afurther year, seven were renewed twice,four three times, and only Fermat fourtimes: in 1644-6, 1648-50, 1655-7 and1663-5. But what attracted Fermat sostrongly to this town on the banks of theriver Agout?

Three reasons can be given. First, acertain sympathy for the ReformedChurch, which can already be observed inhis parents and grandparents. Secondly,Fermats exceptional capability as amediator between conflicting interests,inherited from his father Dominique,which could not show to better advantagethan at a chamber where reconciliationbetween the representatives of the tworeligions had regularly to be sought. Thethird, and perhaps strongest, reason wasthe intellectual atmosphere of Castreswhich, while the seat of the chambre delEdit, saw a golden age of culture that itnever achieved again, before or since.Historians of Toulouse lament theintellectual fall of that town in almost allareas of art and science at that time,particularly with regard to the university,but note as an exception and gloire deToulouse the great scholar Pierre deFermat.

In Castres, in 1648, the ProtestantAcademy was founded with 20 initialmembers who came exclusively from theReformed Church. Most of thesegentlemen were conseillers or avocats of thechambre de lEdit. Among them were thepoets Samuel Izarn, Hercule de Lacgerand Jacques de Ranchin, the theologiansRaymond Gaches and André Martel, thephilosopher Pierre Bayle, the medic,chemist and philosopher Pierre Borel, thephysicist and translator Pierre Saporta,and the historiographer Paul Pellisson, butno mathematician.

Bayle and Pellisson enjoyed nationalreputation, and Saporta and de Ranchinwere Fermats friends. The latter readpoems of Pierre and Samuel Fermat atmeetings of the Academy; to him Fermatdedicated his critical commentary on thework of the Greek historian Polyainos,thereby demonstrating a knowledge ofGreek philology. In 1664 Fermat saw oneof Polyainoss rare works printed,prepared by Saporta; it concerns a shorttext in which Fermat interprets a passagefrom a letter of Synesios of Kyrene. Time

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Coats of arms on one of Picharrots towers. In the lower row are those of four consuls ofBeaumont, elected for the year 1617. Third from left is the coat of arms of the Fermat family

and time again, Fermat felt drawn toCastres; his youngest daughter Louise wasborn there in 1645, and when Fermat diedthere in 1665 his younger son Jean wascanon.

His strong interest in a delegation toCastres did not prevent Fermat frompressing ahead with his professional rise tothe Grand Chambre. By 1647 he wasalready the longest serving conseiller in thefirst chambre des enquêtes and he frequentlytook over the presidency when theprésidents à mortier were both absent.

His move from the first chambre desenquêtes to the Tournelle coincided with theoutbreak of the Toulouse plague epidemicof August 1652 to July 1653. About 4000citizens died - about ten per cent of thetowns population - and Fermat himselfalmost fell victim to the plague. In May1653 the philosopher Bernard Medon,conseiller au présidial de Toulouse and afriend of Fermat, wrote to the Dutch writerNicolas Heinsius the Elder of Fermatsdeath (Fato functus est maximus Fermatius),only to withdraw this news in his nextletter: Priori monueram te de morte Fermatii,vivit adhuc, nec desperatur de ejus salute,quamvis paulo ante conclamata. Fermat wasone of those who became ill with thebubonic plague and survived, but hishealth was weakened from this timeonwards.

Soon after the outbreak of the plagueFermat progressed to the Tournelle,according to the principle of seniority, andfrom there a move to the Grand Chambrewas routine. In November 1654 hebecame a member of the highest chamberof the parliament, and on 9 December heread his first rapport there. In November1655 he was back in Castres, but returnedto Toulouse in November 1657, again tothe Tournelle.

Throughout his life Fermat was a loyalservant of the Crown. Born during theregency of Henry IV, he was a fourteen-year-old boy when the young king LouisXIII spent the night of 24 November 1621in his father Dominiques house inBeaumont-de-Lomagne, while on ajourney from Toulouse to Lectoure. ButFermats impression of his king did notremain unsullied. In 1632 he witnessedthe arrival in Toulouse of Louis XIII, withCardinal Richelieu and 5000 soldiers. Theking forced the Toulouse Grand Chambreand the Tournelle to condemn to death thepopular and highly regarded Duke HenriII de Montmorency because of rebellionagainst the king. The awkward task ofrapporteur in this case fell to the oldestconseiller of the Tournelle, Fermats father-in-law Clément de Long, in whose houseFermat lived at that time with his wifeLouyse.

A stereotype that goes back to Mahoney(see [7, 8]), and has been adopted by morerecent authors, is that Fermat was amediocre conseiller and judge who tried toavoid all social, political and religiousconflicts. Nothing is further from thetruth. Fermat was no jurist who composedlegal treatises, but was an outstandingpractitioner who, tolerant of religious

differences, stood up for justice andhumanity without shrinking fromconfrontations with the mighty, such as thefirst president Gaspard de Fieubet.

In 1648 and 1651 Fermat committedhimself to a rather hopeless fight against

the illegal and brutal methods with whichthe tax collectors (partisans) recovered thetaille from the farmers. On this occasionFermat uncovered the partisans deceitfulpractice of backdating the tax receipts,thereby withholding for themselvesrevenues that were due to the king. In1651, at the time of the Fronde, he was amember of the delegation for theparliament of Toulouse which successfullydemanded (after negotiation for severalmonths) that the delegates of the Estates ofLanguedoc (who took the side of theFronde) should return to a legal state ofaffairs loyal to the king. And on 30 July1652, through a courageous visit to thecamp of the royal army, he prevented hishome town of Beaumont-de-Lomagne(which had been plundered by the soldiersof the Fronde) from being taken by stormand completely destroyed by the kingssoldiers. After the defeat of the Fronde,Fermat achieved through toughnegotiation the outcome that Beaumontshould receive reparation payments of16266 livres. In 1654 Fermat put throughthe Grand Chambre a fairer distribution ofthe income from the charges between theTournelle and the Grand Chambre; in thisway, Fermat made himself unpopular withthe clerics in the Grand Chambre.

Another stereotype is the claim thatFermat never ventured farther thanBordeaux (see [13, p.39]). As we havealready seen, he studied law in Orléansfrom 1623 to 1626. He may also havevisited Paris as a student. Certainly, hisduties as a conseiller forced him toundertake longer journeys; for example, inNovember 1646 the Grand Chambrebanned the dyers of Nîmes from buyinghigh-quality indigo from the Middle Eastinstead of the woad produced aroundToulouse. When the dyers disobeyed theban, Fermat was sent to Nîmes, about 300kilometers to the east of Toulouse, topresent the parliaments decision and

confiscate the forbidden dye-stuff. Thiswasnt a pleasant task for a gentle,retiring, even shy man ([7, Vol. 1, p.22]).Frequently Fermat was assigned to a smallgroup of conseillers who travelled far tomeet bishops, ministers and other

dignitaries, or escorted them a longdistance when they had taken their leave ofToulouse. In such cases Fermatsreputation as a scholar and goodconversationalist was the reason for hisselection.

Certainly Fermat was political, but helacked two important qualities:unscrupulousness and ambition for power.But his abilities as a jurist have also beendoubted by Mahoney (see [7, Vol. 2, p.20])who wrote: The most candid appraisal ofFermats abilities as a jurist, and one thatruns counter to the usual adulation, comesfrom a secret report of Claude Bezins deBésons, intendant of Languedoc, toMinister Colbert in 1663. Speaking of theconseillers and their relations to the suspectFirst President, Gaspar de Fieubet, Bezinsaid of Fermat: "Fermat, a man of greaterudition, has contact with men of learningeverywhere. But he is rather preoccupied;he does not report cases well and isconfused. He is not among the friends ofthe First President". Mahoney then drewnegative conclusions with regard toFermats judicial qualities that have sincebeen adopted without question by otherauthors. If he had investigated morecarefully, such incorrect judgements wouldnot have occurred to him.

In 1965, the legal historian Henri Gillesof Toulouse showed, in a carefulinvestigation which Mahoney obviously didnot read, that Fermat always cultivated avery clear style and that the language of hisarrêts and reports stands comparison withthe style of those written by his colleagues(see [6]). I have convinced myself thatGilles is right. A disparaging judgementby the intendant Claude Bazins de Bessonsis easily explained: in September 1663 theminister Jean-Baptiste Colbert demandedfrom the intendants individual judgementsof all conseillers and other royal officials atthe parliaments. The intendants compliedwith this request so reluctantly that Colbert

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EMS December 2001 15

Epitaph from the former Fermat-mausoleum in the monastary of the Augustins,Toulouse. Year of creation: 1665

asked some intendants for greaterthoroughness. Had Mahoney read thewhole report of 24 December 1663, andnot only an isolated citation in the

accompanying text for an exhibitioncatalogue (see [3, p.33]), he would haverealised how superficial the judgementsturned out to be (see [5, p.111ff]).

De Bessons resided in Montpellier andhad to travel to Toulouse to makeinvestigations and write his report. Therehe first informed himself about theconseillers. By that time Fermat was not inToulouse, but rather in Beaumont orCastres. Therefore de Bessons, turned onbehalf of Fermat to the kings man, thefirst president Fieubet, Fermats enemy.That no fair judgement resulted is notsurprising.

Much more interesting is the reason forthe aversion between Fermat and Fieubet.The judicial murder of a priest, JeanMontralon, was stage-managed by Fieubeton 26 January 1658 (see [1]). This casehad a Jansenist background, and Fermatwas involved in it as rapporteur andexamining judge. Montralon, of whoseproved innocence Fermat was convinced,was hanged next day and his body wasburned. Fermat was so incensed andshocked that he could not work as a judgefor a month. On 6 February 1658, SirKenelm Digby, a notorious liar, reportedon this case to John Wallis in Oxford, but

in form of a wicked slander: that it wasFermat who condemned the priest to beburned alive (see [12, p.808f] and [8,p.360]).

Perhaps because of this event, or becauseof his visibly deteriorating health, Fermatseems to have thought about relinquishinghis office of Conseiller in the GrandChambre. In a letter of 25 July 1660 to theailing Pascal, he proposed that the twomen should meet half-way betweenClermont-Ferrand and Toulouse becausehis health was hardly better than Pascals[10, Vol. II, p.450]). If the latter expectedFermat to travel the whole distance of 300kilometres, then Pascal would run the riskde me voir chez vous et dy avoir deux maladesen même temps.

On 4 March 1660, Fermat wrote his lastwill and testament, with his elder sonSamuel as his sole heir. He amplified thistestament on 13 September 1664, in acodicil in which he made settlements infavour of his wife Louyse: Samuel was topay his mother 32000 livres from theinheritance, an imposing sum which shecould make good use of. Louyse outlivedher husband by more than 25 years. In thepreamble of this codicil Fermat speaksrather openly of his coming end ([4,p.347]): Je soubsigné éstam incommodé dunemaladie qui pourroit avoir de mauvaises suittes.In October 1664 Fermat set off for Castresfor the last time, and died there on 12

January 1665 aged 57 years, afterreceiving the holy sacraments and with analertness of mind to the end. On the nextday he was laid to rest in the chapel of theJacobins in Castres.

The date of Fermats birth is disputed,and there is also confusion about where hismortal remains found their last restingplace. Is it the chapel of the Jacobins inCastres which was demolished soon afterFermats decease? Or is it the familymausoleum in the church of the Augustinsin Toulouse, to which Samuel and JeanFermat had their fathers body moved?After examining all arguments (see [10, 4])I believe that Fermats body wastransferred to Toulouse in the year of hisdeath. But there is no proof. The familymausoleum was destroyed during theFrench Revolution and only Fermatsepitaph, currently restored, has survived.

References1. K. Barner, Eine traurige Episode im Leben

Fermats, Mathematische Schriften Kassel,Preprint No.21/00.

2. K. Barner, How old did Fermat become?NTM, International Journal for History andEthics of Natural Sciences, Technology andMedicine (New series) 8 (4) (October 2001).

3. H. Blaquière & M. Caillet (eds.), Unmathématicien de génie: Pierre de Fermat 1601-1665, Catalogue de lexposition organiséepar la Bibliothèque Municipale deToulouse, Lycée Pierre-de-Fermat,Toulouse, 1957.

4. P. Chabbert, Fermat à Castres, RevuedHistoire des Sciences 20 (1967), 337-48.

5. G.B. Depping, Correspondanceadministrative sous le règne de Louis XIV,tome II, Imp. Nationale, Paris, 1851.

6. H. Gilles, Fermat magistrat. Pierre deFermat, Toulouse et sa région, Actes duXXIe congrès détudes régionales tenu àToulouse les 15 et 16 mai 1965, Fédérationdes Sociétés Académiques et Savantes deLanguedoc-Pyrénées-Gascogne, Toulouse,1966, 35-53.

7. M.S. Mahoney, The Mathematical Career ofPierre de Fermat (1601-1665), 2 vols.,Princeton University Press, 1973, 1974.

8. R. Rashed, C. Houzel & G. Christol (eds.),Oeuvres de Pierre Fermat, Vol. I, Lathéorie des nombres, Albert Blanchard,Paris, 1999.

9. P. Salies, Sur quelques points dhistoiretoulousaine, Mémoires de lAcademie desSciences, Inscriptions et Belles-Lettres deToulouse, 14ème série, 1 (1960), 181-99.

10. P. Tannery, Paul & C. Henry (eds.),Oeuvres complètes de Fermat, Vols. I-IV,Gauthier-Villars, Paris, 1891-1912.

11. L. Taupiac, Fermat: sa vie privée avecpièces justificatives, Bulletin de la SociétéArchéologique de Tarn et Garonne 1879,Forestié, Montauban, 1880.

12. J. Wallis, Commercium Epistolicum, OperaMathematica II, 757-860, Oxford, 1693.

13. A. Weil, Number Theory, An approach throughhistory, From Hammurapi to Legendre,Birkhäuser, Boston, 1983.

Fachbereich Mathematik-Informatik,Universität Kassel, D-34109 Kassel, Germanye-mail: klaus@mathematik.uni-kassel.de

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The house where Fermat was born. Its present shape was given to the property in the 18thcentury. In the background at the top is a 15th-century tower that belongs to the premises.

Since 1996 Professor Novikov has been aDistinguished University Professor in theUniversity of Maryland-College Park, USA.He also keeps strong ties with Russia, occupyingpart-time positions in Moscow; he is a principalresearcher in the Landau Institute forTheoretical Physics and Head of the Geometryand Topology groups in the SteklovMathematical Institute and in MSU. Novikov is a Fields Medallist (1970). TheSoviet Authorities did not allow him to attendthe awards ceremony in Nice as a punishmentfor the letters he wrote supporting people whowere arrested and sent to mental hospitals.Novikov is a member of several academies,including the Russian Academy, the USNational Academy and other Europeanacademies. He is an honorary member of theLondon Mathematical Society, and Doctorhonoris causa of the Universities of Athens andTel Aviv. His works were rewarded throughseveral prizes in the former USSR. During theperiod 1985-96, he was President of theMoscow Mathematical Society, succeeding A.N. KolmogorovThis interview is in two parts the second partwill appear in the March 2002 issue.

What role did your famous family ofNovikovs and Keldyshs play in yourbecoming a scientist?My family played a great role. My father,Petr Sergeevich Novikov, was a famousmathematician. All mathematicians knowhis work on the theory of algorithms andcombinatorial group theory, including theinsolubility of the word problem and thesolution of the Burnside problem fortorsion groups. In the 1930s he was one ofthe best experts in the so-called

descriptive set theory and in the 1940s inmathematical logic. He also started in the1930s a new branch of mathematicalphysics: the reconstruction of ahomogeneous bounded domain from itsgravitational potential at infinity. Mymother, Lyudmila Vsevolodovna Keldysh,was also a prominent mathematician afull professor, and an expert in set theoryand geometric topology.

The family had five children, and I was

the third of them, the youngest of thethree sons. All the sons became physicistsand mathematicians, while the daughterschose other professions. My elder brother,Leonid Keldysh, is one of theinternationally known theorists in solid-

state physics and in condensed matterphysics. My other brother, AndreiNovikov, was an expert in algebraicnumber theory, but unfortunately diedprematurely.

Additionally my mothers brother,Mstislav Keldysh, was a very talentedmathematician in the theory of functionsof a complex variable and in differentialequations. An especially fundamentalcontribution was made by him to appliedbranches of aerodynamics. He was a well-known person in Soviet society, the chieftheorist-adviser of the government and anorganiser of computational work related tojets and space between 1940 and 1960. Allinformation on the work of such peoplewas officially restricted and not reflected inthe world press. For a long time he wasPresident of the Academy of Sciences ofthe USSR. My mothers father,Vsevolod Keldysh, was one of the leadingbuilding engineers in the USSR; he wasmentioned in Nikita Khrushchevsmemoirs.

By the way, Natalia Brusilova, themother of Vsevolod Keldysh (my great-grandmother), was an aunt of the famousRussian general who defeated theAustrians during the First World War (theBrusilov breakthrough, 1916). The dodgyBolshevik leaders Lenin and Trotsky usedhis military talents in their General Staffduring the civil war.

Among the close friends of my parentswere leading Soviet physicists andmathematicians of their generation:I. Tamm, a Nobel prizewinner and teacherof A. Sakharov, M. Leontovich andA. Andronov, applied physicists whoplayed an important role in the countryand who were known in the Soviet physical

and mathematical community as carriersof honour.

Aleksei Andreevich Lyapunov, a pupil ofmy father, a well-known mathematicianand a distant relative of an even morefamous mathematician, organised a DNO(a childrens scientific society), where hischildren, my brother Andrei and I,Vladimir (Dima) Arnold and otherchildren in our familys circle, becameacquainted with the elements of science.A. Lyapunov especially took a greatinterest in some branches of biology thatwere prohibited at that time.

Traditionally, high school students witha talent for mathematics participated inuniversity circles and in Olympiads. I wassuccessful in Olympiads at ages 13 and 14and decided that I could probably becomea mathematician. However, I had nocalling for mathematics and so postponedmy choice of profession until university. Idecided to wait to see whether some otherprofession would attract me. It seemed tome that our family already had a lot ofmathematicians.

I did not choose mathematics as myprofession until I was 17, and I entered theMathematics Division of the Moscow StateUniversity (MGU), the Department ofMechanics and Mathematics.

There are many legends about the famousMGU Department of Mechanics andMathematics in the 1950s and 1960. Couldyou elaborate on the story, please?I learned from my family that one couldgrow into a scientist at voluntaryeducational seminars by solving non-standard problems and studying thingsmissed from the obligatory programmes.

I began to visit such a seminar during myfirst year. It was supervised byV. Uspenskii, a pupil of A. N. Kolmogorovin mathematical logic, who was at that timea young employee at MSU. At this seminarwe studied the complete cycle ofelementary problems in set theory, thefoundations of the theory of functions of areal variable, and the algebra of logic.Soon Sasha (Alexander) Olevskii, myfellow participant at the seminar, becamewell known for his papers on the theory offunctions of a real variable.

During my second year, when I was 18, Ihad to choose a research supervisor for thefirst time and work with him for a year.Only after that, in the third year, was astudent finally allowed to choose hisspecialisation. This rule was in use duringKolmogorovs Deanship of theDepartment of Mechanics andMathematics.

Unlike many of my friends, I chosealgebraic topology. I was probablyattracted by an announcement concerning

INTERVIEW

EMS December 2001 17

Interview with SerInterview with Sergey Pgey P. Novikov . Novikov Interviewer: Victor M. Buchstaber (Moscow)

S.P. Novikov's father P.S. Novikov in 1947

S.P. Novikov's mother L.V. Keldysh withP.S. Alexandrov

a seminar by M. Postnikov, V. Boltyanskii,and A. Shvarts. This announcementaroused the petulance of P. Aleksandrov,the chief Moscow topologist, because set-theoretic topology was placed in anunfavourable light.

In this seminar I began by choosingM. Postnikov as my research supervisorand attended the brilliant lectures ofA. Shvarts, then a postgraduate, in whichthe modern achievements of topology werepresented following the perfectly writtenworks of J.-P. Serre.

During the second and third years Imastered a large collection of moderntopological ideas, with a group of friendsthat included D. Anosov. When I beganmy fourth year, my research supervisorM. Postnikov left Moscow for China foralmost the entire academic year, andA. Shvarts did not get work at MSU as apunishment for the above announcement.We organised a seminar without researchsupervisors: D. Anosov, D. Fuks,G. Tyurina and A. Vinogradov were amongthe participants. In that year (1958-59) Icompleted my first scientific research.

Tell us about the atmosphere at theDepartment of Mechanics and Mathematicsat that time and on its formative influenceon you as a scientist.At the Department of Mechanics andMathematics there was a creative spirit,and an anxiety on the part of the studentsto start scientific activity as soon aspossible.

Completing my third year at the age of20, I encountered the following situation atthe Department of Mechanics andMathematics: those who had chosen areasrelated to the theory of functions of a realvariable were already authors of well-known scientific works. Some of them,members of the Kolmogorov seminar, hadeven written famous works.

In algebraic topology the situation wasquite different: Moscow was not then at thecentre of this area. Especially after thedeparture of Shvarts, I had to find my wayto science without help from researchsupervisors.

How were your first works written? Amongthem was the well-known Milnor-Novikovtheorem on the complex cobordism ring.How does one begin? The most difficulttask is to produce ones first scientific work,especially if one has no supervisor such asKolmogorov who can quickly introduceone to the very centre of mathematics andindicate problems that are both deep andaccessible.

My approach to this problem was asfollows: one must take some newoutstanding work that has not yet beenstudied in detail by the community and trywith great effort to study it in depth. If youare successful, then you will be at homewith methods almost all the experts in yourarea are out of touch with. In this case youwill soon succeed in doing something new.This I did, by studying the remarkableworks of Frank Adams and Rene Thom in1958.

Bizarre homological calculations withspecial Hopf algebras formed a quiteremarkable area that was then absolutelyunknown, outside a narrow circle ofalgebraic topologists. Many years later,when the importance of Hopf algebrasbecame known to everyone, people evenforgot who first discovered these objects: itwas actually Armand Borel (rather thanHopf) in 1954, but for a rather narrowerpurpose, the homology of Lie groups andH-spaces.

Hopf algebras of a new Steenrod typewere discovered by John Milnor in 1957.In Adams works, they began to give deepresults for the problem of Hopf invariants.I was the first (as well as J. Milnor) to applythis technique in cobordism theory,extremely successfully. At that time, intopology, refined algebraic manipulationsbecame tightly mixed up with thegeometry of function spaces, involving thetheory of manifolds and usingfundamental ideas of transversality,cobordism and the calculus of variations.

My first works were published in 1959-60 and became well known. Thetechniques of Hopf algebras and newhomological constructions were applied tothe calculation of homotopy groups ofspheres and of cobordism groups. Themost significant results were my theoremson the evaluation of cobordism rings, andthe very ideas of cobordism were greatlyextended.

By 1960, after all this work, I began tofeel like a mature scientist and decided toturn my efforts to a new area, differentialtopology.

I well remember the great impressionproduced by your report at the 1966

International Congress of Mathematiciansin Moscow. It was related to your earliestwork, and the Adams-Novikov SpectralSequence and Landweber-Novikov algebrashad developed from your first interests.Yes. Some years after I returned to thistopic, in 1966-68, I reconsidered themethods of algebraic topology from theviewpoint of the theory of complexcobordism. The interaction ofhomological algebra with the geometry ofmanifolds adds a special elegance to this

area. In particular, in collaboration withmy student A. Mishchenko, in 1967 webegan to apply formal groups in topology.This idea was soon picked up by D. Quillen(1969), who made an importantcontribution. In collaboration with mystudent, V. Buchstaber, we introduced theidea of a multi-valued formal group(1971). Later, the theory of these objectsand their topological applications wereconsiderably developed by V. Buchstaber.In collaboration with my studentsV. Buchstaber, S. Gusein-Zade andI. Krichever, we started anotherinvestigation in which formal groups wereintensively used to study finite andcompact transformation groups; this gavean alternative approach to the Atiyah-Bott-Hirzebruch analytic methods. Theseresearches were decades ahead of theirtime.

However, as is well-known, you alsoreturned to this topic later?Yes. In the last decade you and I have hadoccasion to return to this area inconnection with the theory of quantumgroups and other algebraic problems. Thestore of algebraic ideas originating fromcomplex cobordism theory is still far fromexhausted.

Lets return to the Department ofMechanics and Mathematics in the early1960s.Having completed my first work I becameactively interested in what was happeningaround me in the Department ofMechanics and Mathematics, and outsidetopology. Dima Anosov drew my attentionto the geometry and topology of dynamicalsystems, and I began to study this area. In

the late 1950s, I. Gelfand suggested that S.Dynin should consult me about algebraictopology in connection with the indexproblem for elliptic operators, and thishelped him to produce good results forwhich he was awarded the prize of theMoscow Mathematical Society. The indexproblem was already becomingfashionable, and so I began to masterpartial differential equations andfunctional analysis with the help of myfriends, especially Boris Mityagin.

INTERVIEW

EMS December 200118

S.P. Novikov with some of his students in Edinburgh in 1998: from left B. Dubrovin,P. Akhmetev, V. Buchstaber, S.P. Novikov, S. Tsarev, A. Veselov, I. Krichever, O.

Mokhov, I. Taimanov. James Clerk Maxwell is lurking in the background.

In 1962 the famous work of Atiyah andSinger appeared, which increased thepublics interest in topology. Smalesdiscoveries in 1961 significantly increasedthe role of topology in explaining

complicated dynamical systems, and theworks of Grothendieck, Hirzebruch, Atiyahand Milnor brought topology andalgebraic geometry together.

After this, I began to study differentareas of mathematics, actively attendingseminars by I. Gelfand, V. Arnold,I. Shafarevich, M. Vishik and others. Inturn, they asked me for help with moderntopology.

This was precisely the atmosphere of theDepartment of Mechanics andMathematics at that time, to help eachother to master new ideas and the methodsof different areas in the simplest and bestway, and to explain ideas to one anothertransparently, without artificialcomplexities.

At that time, the Department ofMechanics and Mathematics of MSUrepresented all branches of pure andapplied mathematics. I do not know of anysimilar scientific group assembledanywhere in the West after the SecondWorld War.

What about your results on theclassification of manifolds? What isBrowder-Novikov theory?I was greatly impressed by Milnorsremarkable discovery of smooth structureson the 7-dimensional sphere, togetherwith the classification theory of manifoldsthat are homotopy spheres. During theacademic year 1960-61 I studied thewritings of Whitney, Pontryagin, Thomand Milnor, all of which are written withgreat clarity. The completeness of theproofs in these papers was achieved withno detriment to understanding andwithout any artificial formalisation.

In the summer of 1961 I met the starsof world topology: Milnor, Hirzebruch andSmale, who came to the USSR for variousconferences as the iron curtain gradually

began to rise. These meetings were ofgreat importance for me since they showedme the frontiers of differential topology.After my meeting with Smale at the SteklovMathematical Institute, where I was apostgraduate, my local superiors began toregard me as a serious scientist.

Very soon, in the autumn of 1961, Imanaged to make a decisive breakthroughin the classification problem for simplyconnected manifolds with dimensiongreater than 5. This result wasacknowledged as the best mathematicalwork in the Academy of Sciences of theUSSR for that year.

Specifying the homotopy invariants of asimply connected manifold and theintegrals of the Pontryagin classes over thecycles, you can determine the manifolduniquely up to finitely many possibilities.The description of this finite set is ratherdelicate, and I shall not dwell on it here:the set can be completely evaluated interms of homotopy groups of the Thomspace of the normal bundle describingspecial cobordisms of normal maps ofmanifolds of degree 1. These maps areanalogous to the birational smooth mapsin algebraic geometry. They have aremarkable topological property, which isthe basis of the method. This techniquewas discovered independently by Browderin 1962 while solving another problem.

The evaluations in concrete examplesled me to interesting conclusions. Forinstance, it follows from one of thesecalculations that the group ofdiffeomorphisms of the 8-dimensionalsphere (to be more exact, the connectedcomponent of this group) cannot becontracted to the orthogonal subgroup.The PL-classification of manifolds alsofollows from these methods. As far ascontinuous homeomorphisms areconcerned, the problem must be discussedseparately.

We now come to your famous theorem on thetopological invariance of Pontryaginclasses and to the Novikov conjecture onhigher signatures.Continuous homeomorphisms differsubstantially from smooth and piecewise-linear ones. For instance, the property ofa map to be a diffeomorphism is stable inthe C1 topology: any map that is sufficientlyC1-close to a diffeomorphism is also adiffeomorphism. This is not true forcontinuous homeomorphisms ofmanifolds: perturbing a homeomorphismin the C0 topology, one can obtainsomething very complicated buthomotopic to the identity map.

While establishing the topologicalinvariance of various quantities (homologyand cohomology, Stiefel-Whitney classes,etc.), the methods of classical algebraictopology led to a stronger theorem, thatthese quantities are in fact homotopyinvariants. This property is stable.

For simply connected manifolds, theintegrals of Pontryagin classes over thecycles are certainly not homotopyinvariant. For this reason, the problem oftheir topological invariance (with respect

to continuous homeomorphisms ofmanifolds) occupied a special place intopology. Incidentally, as Milnor-Kervaireshowed in 1962, the complete Pontryaginclass regarded as an integral cohomologyclass is not invariant under PL-homeomorphisms. The topologicalinvariance is established only for theintegrals of these classes over those cyclesthat can be expressed via a Riemannianmetric.

I managed to prove this conjecture in1965 by using a sophisticated techniquebased on all the achievements of algebraicand differential topology. The ideaconsisted of a construction that is, in asense, similar to the so-called étaletopology of Grothendieck. Working withsimply connected manifolds, I artificiallyintroduced toric neighbourhoods of cyclesand constructed differential topology intheir coverings. Notably, in subsequentworks (by Kirby and others) where otherknown problems in topology of continuoushomeomorphisms were solved, thepresence of toric constructions wasobligatory. Thus, all integrals ofPontryagin classes over cycles turn out tobe topologically invariant.

As a rule, they are not homotopyinvariant. For simply connected manifoldsthere is only one homotopy invariantexpression in Pontryagin classes, namelythe Hirzebruch formula for the so-calledsignature of the manifold the importanthomotopy invariant characteristic ofcobordism discovered in the early 50s byR.Thom and V.Rokhlin.. Its importance intopology, in algebraic geometry, and in theindex theory of elliptic operators is wellknown. I observed that, if the fundamentalgroup is non-trivial, then there are non-trivial cohomology classes with thefollowing property: if we multiply this classby the Pontryagin-Hirzebruch polynomialand integrate over the entire manifold,then the result is homotopy invariant; forexample, products of one-dimensionalcohomology classes have this property.

In the course of my proof of topologicalinvariance of the Pontryagin classes, Ineeded to establish some special cases ofthe above statement. Around 1967 myconjecture concerning products of one-dimensional cohomology classes wascompletely proved by a number of authors(V. Rokhlin, G. Kasparov, W-C. Hsiangand T. Farrell). In 1970 I formulated thegeneral conjecture, that this propertyholds for any Eilenberg-MacLane cocyclethat sits on the fundamental group thatis, it arises from homological algebra. Thecorresponding integral (over the entiremanifold) of the product of this class withthe Pontryagin-Hirzebruch class isreferred to as a higher signature. Myconjecture also includes the hypothesisthat the higher signatures exhaust allhomotopically invariant expressions of thecurvature tensor.

For the past 30 years, this conjecture hasbeen studied in many works in whichhomological algebra has become mixedwith the theory of infinite-dimensionalrepresentations and functional analysis.

INTERVIEW

EMS December 2001 19

S.P. Novikov in 1974

The conjecture has been proved forhyperbolic groups, for discrete subgroupsof Lie groups, and in some other specialcases.

In the late 1960s and the early 1970s, Ideveloped ideas for a special algebraicanalogue of symplectic geometry (which Icalled a Hamiltonian formalism over ringswith involution); I thought that theexplanation of higher signatures and ofother deep properties of multiplyconnected manifolds had a symplecticorigin. However, research by topologistsinto the problem of higher signatures useda different approach.

In 1971 I. Gelfand went into myalgebraic ideas: they impressed himgreatly. In particular, he told me of hisobservation that the so-called vonNeumann theory of self-adjoint extensionsof symmetric operators is simply the choiceof a Lagrangian subspace in a Hilbertspace with symplectic structure. Manyyears later, in 1997, I used this idea in mywork involving scattering theory ongraphs.

Did you work in the topology of low-dimensional manifolds? Is it true that yourclassical theorem on the theory of foliationsis purely topological?In 1963, under the influence of friendsworking in dynamical systems (especiallyV. Arnold), I developed the qualitativetheory of codimension-1 foliations onmanifolds, and managed to find deepresults for two-dimensional foliations ofthree-dimensional manifolds. Inparticular, I proved the well-knownconjecture that every non-singularfoliation of the three-dimensional sphereS3 has a compact leaf; in fact, I proved thata foliation on S3 always contains a tube that is, a two-dimensional torus filled witha special Reeb foliation. The complete setof these Reeb components is necessarilyknotted. We still do not know which knots(linkages) can serve as a complete set ofReeb components of a non-singularfoliation on S3.

I gave a topological classification ofanalytic foliations in the solid torus interms of tree-like sequences of conjugacyclasses in braid groups. Using braids,Zieschang and I showed in 1963 that anon-singular foliation exists on any three-dimensional manifold. I also managed tofind the first non-trivial topologicalcondition on a three-dimensional manifoldadmitting an Anosov system withcontinuous or discrete time; for example,for discrete time the manifold must behomeomorphic to a 3-torus. The Anosovfoliations arising here are not smooth ingeneral, and so direct topological methodsare necessary. This work originally had agap (indicated by Anosov) which was filledby my student A. Brakhman in 1968.

You have recently considered topologicalproblems arising from the physics of metals.What is the Novikov problem concerningthe motion of electrons along a Fermisurface, and how is it connected with realphysics?

In 1982 I became interested in afundamental geometric picture arising inthe theory of metals. Each crystallinemetal has a Fermi surface, a level surfaceof a Morse function on a three-dimensional torus corresponding to thedual lattice; this torus is called the quasi-

momentum space. The only electrons ofimportance for electrical conductivity atlow temperatures are free electrons closeto the Fermi surface. In a magnetic field,electrons begin to move along the Fermisurface. The trajectories of their motionon the universal covering R3 look like theintersections of the Fermi surface byplanes perpendicular to the magneticfield. This dynamical system on the Fermisurface can be extremely complicated ifthe image of the fundamental group coversthe entire lattice. To this end, the genus ofthe Fermi surface must be not less than 3.It is interesting that some metals (gold,copper, lead and platinum) satisfy thiscondition.

Many years ago, the well-known Sovietphysicist I. Liftshitz and his school(M. Azbel, M. Kaganov, V. Peschanskiiand others) formulated the principle ofgeometric strong magnetic field limit,which states that all essential properties ofelectrical conductivity in strong magneticfields are determined by the abovedynamical system on the Fermi surface. Innormal metals, this description works formagnetic fields that do not exceed 103T(107 Gauss). What is the geometry andtopology of this dynamical system? Is thissystem useful or not? These problemshave been investigated at my seminar formany years since 1982. The work of mystudents A. Zorich, I. Dynnikov andS. Tsarev helped to overcome the maintopological difficulties in 1984-1993.

However, my student A. Ya. Maltsev andI have recently established that thetopological facts can be combined in anextremely successful way so as to lead tophysical conclusions. It turns out that theconductivity in a strong magnetic fieldeither vanishes or has a very special formcharacterised by a triple of topologicalintegers. These three numbers aretopologically stable, being preserved

under small perturbations of the directionof the magnetic field. This picture holdsfor a set of full measure (in the two-dimensional sphere) of directions of themagnetic field. For those particulardirections for which this picture fails, thesituation can be incomparably more

complicated. According to my conjecture,these particular directions form a setwhose fractal dimension is less than 1.

Behind this picture lie beautiful anddeep theorems of three-dimensionaltopology. The observable triple of integersis in fact a two-dimensional homology classof the three-dimensional torus, called thesupport of the open trajectories. Forthese physical systems, it turns out that thecompetition between topological completeintegrability and stochasticity is won byintegrable systems for the overwhelmingmajority of magnetic fields. Only a set ofsmall fractal dimension are stochasticsystems, and the investigation of thiscomplicated set requires deeper analyticaland numerical tools and exceeds the limitsof standard differential topology.

Your research in metal physics has involvedboth topology and non-linear dynamics.What has been your experience ininteracting with both mathematicians andtheoretical physicists?When working with physicists, I haveaimed to find points of contact betweenscience and the ideas and methods ofmodern mathematics that had notpreviously been used outside puremathematics.

I was not interested in providingrigorous mathematical justification forresults already obtained by physicists. Imanaged to find applications of topologyand non-linear dynamics, of analysis onRiemann surfaces (algebraic geometry),and of some non-standard aspects ofRiemannian geometry, in some areas oftheoretical and mathematical physicswhere nobody expected such applications.Moreover, I have helped some prominentphysicists, A. Polyakov, I. Dzyaloshinskii,G. Volovik and others, to apply topology inthe theory of Yang-Mills fields andcondensed matters physics.

INTERVIEW

EMS December 200120

S.P. Novikov and M.F. Atiyah in Edinburgh in 1998

Jacques-Louis Lions was born in the heartof Provence in the charming city of Grasse,much renowned for its perfume industryand its historical centre.

In spite of his young age, he had thecourage and determination to join theFrench Résistance at the end of 1943, as asoldier in the FFI (French Forces of theInterior). There he met Andrée, his wifeand life-long companion.

Their son Pierre-Louis, who was born in1956, would also be distinguished by

mathematical talent. This gift earned himthe highest mathematical distinction, theFields Medal, awarded to him during the1994 International Congress ofMathematicians in Zürich. His parentshad the great joy of being present on thisunique occasion.

At the early age of nineteen, Jacques-Louis Lions passed the entrance exam tothe highly coveted École NormaleSupérieure de la rue dUlm. There he metBernard Malgrange, among others, and atthe end of their studies they both decidedto opt for a university career inmathematics (a rather uncommon choiceat a time when most Normaliens wouldrather teach the famed classes deMathématiques Spéciales in the lycées).They were then awarded a grant by CNRS(the National Centre for ScientificResearch) to prepare their doctoraldissertations, and went to Nancy to workunder the guidance of a prestigious thesisadvisor, Laurent Schwartz, who had justreceived the Fields Medal for his theory ofdistributions in 1950.

After defending his thesis in 1954,Jacques-Louis Lions began his career enprovince (outside the Paris region) as wasthen customary, at the University ofNancy, where he held a professorship from1954 to 1962.

Far from keeping him fully occupied, hisremarkable mathematical achievementsduring that period left him enough time toenvision the immense opportunitiesoffered by scientific computing, which wasthen coming of age, with the manifoldindustrial applications that wouldhenceforth become amenable. Thisconstant quest for applications, that wouldguide him all his life and become one ofthe most exceptional aspects of his career,materialised in 1958 when he becamescientific consultant for the SEMA (Societyfor Economics and Applied Mathematics),a society headed by Robert Lattès, who hadentered the École Normale Supérieure oneyear after him. While such inclinations arecommon nowadays, it required lots ofcourage to follow them at that time. Theapplications of mathematics did not thenarouse the enthusiasm that they nowgenerate!

After Nancy, Jacques-Louis Lions wasnamed professor at the University of Paris,where he very quickly created a weeklyseminar on Numerical Analysis, adiscipline that was practically unheard ofin France at that time. This seminar firstmet in the basement of the Institut HenriPoincaré, then in a dusty room of theInstitut Blaise Pascal, which was situated inthe rue du Maroc in the North of Paris.

When the University of Paris split intothirteen distinct universities, he chose thesixth one, which was later to be named theUniversité Pierre et Marie Curie. Two ofhis major initiatives there were to foundthe Laboratoire dAnalyse Numérique(after thirty years on the Jussieu campus,this department was relocated in 1999 inthe rue du Chevaleret, near Place dItalie)and to create a DEA (Diplome dEtudesApprofondies, a set of advanced coursesthat a doctoral student has to pass beforebeginning a dissertation), specialising inNumerical Analysis. This DEA, fromwhich a considerable number of appliedmathematicians now holding positions inuniversities, at CNRS, or in industry, havegraduated over the years, was always highlyregarded. The degree is now one of themost successful components of theJussieu-Chevaleret Doctoral School ofMathematical Sciences, headed by YvonMaday.

In 1973, at the early age of forty-five,Jacques-Louis Lions had the highlyunusual honour of being named professorat the celebrated Collège de France andsimultaneously elected to the FrenchAcademy of Sciences. At the Collège de

France, he held the Chair in MathematicalAnalysis of Systems and of their Control,for twenty-five years. His series of lectures,which in the tradition of the Collège had tobe renewed each year, were alwaysattended by vast audiences, attracting notonly his own students but also the studentsof his students!

The Seminar in Applied Mathematicsthat he organised there until 1998, firstwith Jean Leray and then with HaïmBrezis, soon became an institution withinan institution. Indeed, countless appliedmathematicians, from Paris and its vicinityand French and foreign colleagues visitingParis, gathered each Friday afternoon tohear prestigious lecturers, such as StuartAntman, John Ball, Felix Browder, CiprianFoias, Gu Chao-hao, Li Ta-tsien, KlausKirchgässner, Peter Lax, Andrew Majda,Louis Nirenberg, Olga Oleinik, SergeiSobolev, Tosio Kato, Mark Vishik, andmany others.

From 1966 to 1986, Jacques-Louis Lionswas also part-time professor at the ÉcolePolytechnique, where he created a coursein numerical analysis from scratch, thatsoon became a legend! Following the ruleat the École Polytechnique, he also wrotelecture notes whose contents wererevolutionary for the time, at least inFrance. Indeed these notes constituted akind of encyclopaedia in which, with hisnatural gift for teaching, Jacques-LouisLions described and analysed practicallyall that was then known about thenumerical analysis of partial differentialequations. Introductions to numericaloptimisation and numerical linear algebrawere also presented in two separatechapters written by his first two doctoralstudents, Jean Céa and Pierre-ArnaudRaviart. A mystery remains about the firstversions of these lecture notes: they wereaffectionately referred to as theDiplodocus, even though no-one(including their author) ever seemed tounderstand why!

But all of these essentially academicactivities that would normally occupy all ofones time did not take up all of his. Farfrom it! From 1980 to 1984, he was alsoPresident of INRIA (National Institute forResearch in Computer Science andAutomatics), normally a full-time position!His leadership was of profound and lastinginfluence at INRIA. During his first weeksat the head of this institute, he used hisincredible talents as an organiser torejuvenate the organisation and objectives in particular, by introducing the notionof a project, gathering a clearly identifiedteam around a well-defined objective on aspecific theme.

During his four-year term as president,he strongly advocated the creation of start-up companies by researchers from theinstitute and he initialised itsdecentralisation through the creation ofsimilar institutes at Sophia-Antipolis andRennes. Through his personal prestige,the teams he was able to gather, and thenumerous first-class internationalconferences that he organised there, hegreatly contributed to the fame of INRIA.

OBITUARY

EMS December 2001 21

Jacques-Louis Lions (1928-2001)Jacques-Louis Lions (1928-2001)Philippe G. Ciarlet (Paris)

Photo: Collège de France (J.-P. Martin)

From 1984 to 1992, he held anotherhigh-level, and also normally full-time,official position as President of CNES(National Centre for Space Studies), wherehe continued and developed the action ofhis predecessor Hubert Curien, who hadjust been named Minister of Research andTechnology. There he used not only hiseminent intellectual capacities but also his

talents for intelligent persuasion toconvince the French authorities that thedirections that he advocated were wellfounded. In this way, he played a majorrole in the conception of the French-American Topex-Poseidon spaceprogram for oceanography. Topex-Poseidon is also the name of the satellitethat made it possible at last to understandEl Niño, a major event in climatology.His influence was likewise a decisive factorin the French-Russian negotiations thatultimately allowed Jean-Loup Chrétienand Michel Tognini to participate inmanned space missions.

For many years his presence at theMonday afternoon seances of the FrenchAcademy of Sciences were rare. But heeventually gave new life to this nobleCompagnie (as it is traditionally knownamong its members) when he becamePresident in January 1997 for thecustomary two years. Immediately afterLions took office, President Jacques Chiracgave him the mission of supervising thedrafting of a document concerning thestate of the art world-wide in each of thefollowing areas: access to knowledge for alland electronic processing of information;knowledge of our planet and ways of life;and understanding life systems andimproving health-care for all. Heimmediately began to work on thisambitious undertaking by creating andheading a Committee 2000, under hisongoing close supervision, whose task wasto analyse the three areas and makeproposals. Remarkably, in spite of thescope of this project, he was able to meetthe 2000 deadline he had set himself, andpersonally handed President Chirac therequested document during a ceremony atthe Elysée Palace on 25 January 2000. Heeven succeeded in having all the Membersand Corresponding Members of theAcademy invited for the occasion, a firstindeed!

However, Jacques-Louis Lionss actions

during his presidency were not limited toCommittee 2000. His efforts were alsodecisive in promoting the need for aprofound reform in the status of theAcademy; the principles of this reformhave now been accepted. He also played amajor role in the creation of an Academyof Technology, always desired but neverpreviously achieved. This academy waseventually created on 12 December 2000.

As exemplified by his presidencies atINRIA and CNES, Lions was anexceptionally successful promoter of ever-closer ties between academic research, toooften seen as disconnected from the realworld, and the more pragmatic industrialresearch. In this spirit, he headedscientific committees in major public utilitycompanies, such as MétéorologieNationale, Gaz de France, France Telecomand Electricité de France, and he heldhigh level advisory positions in majorcompanies, such as Pechiney, DassaultAviation, or Elf.

Jacques-Louis Lionss influenceextended far beyond frontiers. Since thebeginning of his career, he was anindefatigable traveller who, in addition tothe traditional venues in Europe and theAmericas, very quickly added moreunusual ones to his list of destinations. Forinstance, as early as 1957 he set out for athree-month visit to the Tata Institute ofFundamental Research in Bombay at thetime a genuinely adventurous trip! Heenjoyed the splendour of the ancient TajMahal Hotel and the hospitality ofKollagunta Gopalaiyer Ramanathan, withwhom he contributed to the creation of anapplied branch of the Tata Institute on thecampus of the Indian Institute of Sciencesin Bangalore, twenty years later.

In 1966 he began an extended series ofvisits to the former Soviet Union.Frequently invited by the USSR Academyof Sciences or by the Novosibirsk Institutefor Computation, he initiated manyscientific exchanges with eminent sovietmathematicians such as Guri Marchuk,Olga Oleinik, Lev SemenovitchPontryagin, Ilia Vekua, Mark Visik andNicolay Nicolayevich Yanenko. One of hismerits during this period, and not theleast, was to contribute greatly to thedissemination in the West of Sovietresearch in applied mathematics. Oneparticular trip that left him with a lastingimpression was the journey that heundertook in 1975 to Beijing, where hewas received with great ceremony. He wasparticularly impressed there by themathematical talents of Feng Kang, whohad just independently rediscovered thefinite element method. He was alsoimpressed by Feng Kangs impetuositywhen he spoke about the Gang of Four!

However, his international ventures werenot limited to traditional scientificexchanges, as his talents as a lecturer,thesis adviser, and organiser producedmany disciples throughout the countrieshe visited. As early as the 1960s, forinstance, he was the adviser of AntonioValle, the first in a long series of studentsfrom Spain and Portugal, who in turn set

up numerical analysis departments at theUniversities of Malaga, Sevilla, Santiago deCompostela, Lisboa, and at theUniversidad Complutense de Madrid,modelled after the one he had created inParis. In the same vein, he was the mainspeaker in a 1997 European video-conference on Mathematics and theEnvironment, organised in Madrid byJesus Ildefonso Diaz. He also chaired thePrize Committee that awarded the tenPrizes for Young Mathematicians, duringthe Third European Congress ofMathematics, held in Barcelona in 2000.

For many years, he also chaired theScientific Committee of the Istituto diAnalisi Numerica del CNR of theUniversity of Pavia, headed for severaldecades by Enrico Magenes and then byFranco Brezzi.

Together with Paul Germain, herepresented France at the 1975 meetingon Functional Analysis and Mechanics ofthe IUTAM (International Union forTheoretical and Applied Mechanics), heldin Luminy, where the other representativeswere Klaus Kirchgässner from WestGermany, Sir James Lighthill from theUnited Kingdom, and William Pragerfrom the United States.

His intelligent proselytising was notlimited to Europe, however. In China, forinstance, he was one of the driving forcesbehind the creation in 1997 of the LIAMA(French-Chinese Laboratory of ComputerScience, Automatics, and AppliedMathematics), an offspring of INRIA andAcademia Sinica, housed ever since by theInstitute of Automatics of the Academy ofSciences in Beijing. He likewise played amajor role in the creation in 1998 of theISFMA (Chinese-French Institute ofApplied Mathematics), splendidly housedby the Department of Mathematics ofFudan University in Shanghai, thanks tothe tireless efforts of its Director Li Ta-tsien.

From 1991 to 1995 Jacques-Louis Lionswas President of the IMU (InternationalMathematical Union). During a meetingof this organisation in Rio de Janeiro, on 6May 1992, he proposed that the year 2000be named World Mathematical Year.This proposal, which was later supportedby UNESCO, turned out to be a genuinesuccess story that significantly contributedto the improvement of the image ofmathematics among the general publicand helped to encourage mathematicalresearch in developing countries.

He likewise was a constant supporter ofthe initiatives of the Third World Academyof Sciences (TWAS), either directly orthrough colleagues from his group.Particularly noteworthy in this respectwere his undertakings for the progress ofmathematical research in Africa.

The mathematical works of Jacques-Louis Lions are immense. Alone, or incollaboration, he wrote more than twentybooks, most of which have become classics(often translated into several foreignlanguages), as well as more than fivehundred papers. The different themes ofhis work are briefly described below, in

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approximately chronological order.He had, and will continue to have for a

long time, a considerable influence onmathematics and its applications, not onlythrough his own work, but also throughthat of the School he created andconstantly kept in touch with. Over theyears this School, which numbered somefifty initial students and scores of studentsof students, etc., has acquired widespreadfame, not only in university circles, but alsoin industry an accurate indication thatthe directions of research he envisionedand promoted were highly relevant.

If a single title were to be attached toJacques-Louis Lionss mathematical works,it might be with a fair degree of accuracythat of Partial differential equations in alltheir aspects: existence, uniqueness,regularity, control, homogenisation,numerical analysis, etc., and theapplications they model, such as fluid andsolid mechanics, oceanography,climatology, etc..

Jacques-Louis Lions produced his firstmathematical works in 1951. At the sametime, two major books were published, oneby Laurent Schwartz on the theory ofdistributions and one by Sergei Sobolev ontheir applications to mathematical physics,as well as a founding paper by John vonNeumann and Robert Richtmyer on thenumerical approximation of non-linearhyperbolic problems arising inhydrodynamics.

Inspired by these works, Lionss firstobjectives were to undertake a systematicstudy of linear and non-linear boundaryvalue problems notably, by constantlyusing the theory of distributions, and thenfinding ways to numerically approximatetheir solutions.

In 1954, he began a series ofcollaborations and lasting friendships witheminent Italian mathematicians, such asEnrico Magenes, Guido Stampacchia,Ennio de Giorgi and Giovanni Prodi(brother of the current President of theEuropean Union). One such collaborationresulted in an exhaustive analysis ofboundary value problems posed infractional Sobolev spaces, due in particularto the theory of interpolation betweenBanach spaces that he initiated with JackPeetre in 1961. This analysis is the objectof the celebrated three-volume treatiseNon-homogeneous boundary value problemsand applications (1968-70) that he wrotewith Enrico Magenes. From 1965 to 1967,he developed with Guido Stampacchia thefoundations of the theory of variationalinequalities, as they appear (for instance)in unilateral problems in elasticity.

His inclination towards applications ledhim to propose a particularly elegant proofof Korns inequality, based notably on afundamental result in distribution theoryknown as Lionss lemma (althoughseveral other results of his bear the samename!). He further developedapplications of the theory of variationalequations or inequalities to mechanics, bymathematically analysing Bingham fluid,friction, viscoelasticity and plasticitymodels. These applications constitute the

substance of another well-known book,Inequalities in mechanics and physics (1972),that he wrote with Georges Duvaut.

He was equally interested in thenumerical simulation of these problems, at

a time when it was realised that theapplicability of finite difference methodshad reached its limits; for instance, thesemethods do not perform well when theproblems to be approximated have rapidlyvarying coefficients or are posed ondomains with complicated geometries. Onthe other hand, the finite element method,already familiar to engineers whenhandling these types of difficulties,remained essentially unknown tomathematicians.

With remarkable intuition, Jacques-Louis Lions immediately foresaw that it ispreferable to discretise the variational, orweak, formulations of partial differentialequation problems, rather than the partialdifferential equations themselves.Accordingly, he quickly pointed out to hisgroup of colleagues and students the needfor studying and analysing Galerkinmethods in general, and finite elementmethods in particular. A productiveperiod ensued, to which he himselfcontributed with another classic, Numericalanalysis of variational inequalities (1976), co-authored with Roland Glowinski andRaymond Trémolières.

His 1969 book Some methods for solvingnon-linear boundary value problems was amajor contribution to the theory of non-linear partial differential equations, whicheven today remains a substantial source ofinspiration it is unfortunate that thisbook was never translated into English. Inthis work, Lions introduced andsystematically analysed the so-calledcompactness methods, which play a keyrole in the existence theory for the Navier-Stokes and von Kármán equations, themonotony methods he had developed withJean Leray, and the regularisation andpenalty methods, which can for instance beapplied to the Schrödinger or Korteweg-deVries equations. For the most part, theresults found in this book are either due tohimself or to his students in particular,Haïm Brezis and Luc Tartar.

Most of the works mentioned so far,together with the many generalisationsthey led to, were assembled in themonumental treatise Mathematical analysisand numerical methods for sciences andtechnology (1984-5), conceived and edited

by Jacques-Louis Lions and RobertDautray. This work, which comprisesalmost four thousand pages, is justlyregarded as the modern counterpart of thecelebrated Courant-Hilbert work.

His on-going interest in problems withsmall parameters led him to write Singularperturbations in boundary value problems andin optimal control (1973), in which he laiddown the foundations of the asymptoticanalysis of such problems. The methodsand notions that he then introduced andanalysed, such as a priori estimates, stiffproblems, boundary layers, multiple scales,and so on, were subsequently recognised asfundamental for many applications; forinstance, they later played a major role inthe mathematical modelling of elasticstructures and multi-structures made ofplates, rods or shells.

Another field where small parametersarise naturally is in the modelling ofcomposite materials of constant use inthe aerospace industry, for instance. Theirasymptotic analysis, a special case of whatbecame known as homogenisation theory,was abundantly developed and illustratedby applications in another seminal work,Asymptotic analysis for periodic structures(1978), which he wrote with AlainBensoussan and George Papanicolaou. Inthis book, a substantial number ofessentially empirical formulas used in themodelling of periodic structures wererigorously justified for the first time,thanks notably to the compensatedcompactness method of his studentsFrancois Murat and Luc Tartar and to theoscillating test-functions method of LucTartar.

In 1958, a fundamental work by LevSemenovitch Pontryagin on the optimalcontrol of systems governed by ordinarydifferential equations (the objective was tocontrol the trajectories of artificialsatellites) immediately attracted hisattention. Through the contacts healready had at that time with theengineering community, he quicklybecame convinced that the next step was toextend optimal control to distributedsystems systems whose state is governedby partial differential equations. Theinclination that he then developed for theoptimal control of such systems was alwaysto remain at the centre of his mathematicalinterests.

A pioneer, as always, he began by layingdown the foundations of a general theoryin yet another celebrated book, Optimalcontrol of systems governed by partialdifferential equations (1968), in which henotably introduced an infinite-dimensionalversion of the Riccati equation.

In two books co-authored with AlainBensoussan, Applications of variationalinequalities to stochastic control (1978) andImpulse control and variational inequalities(1983), he continued his investigations byconsidering in particular the optimalcontrol of systems that are not necessarilywell posed, or that have multiple states.

After having so thoroughly analysed themain aspects of optimal control theory,Lions shifted his interests to the study of

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controlability, a discipline that basicallyseeks to answer the following type ofquestion: given a system in an arbitraryinitial state, how can one devise a way ofacting on it in such a way that its solutionreaches a given final state in a finite time for instance, by imposing adequateboundary conditions?

During his prestigious John vonNeumann Lecture at the SIAM Congressin Boston in 1986, he presented for thefirst time his now-famous HUM (HilbertUniqueness Method) for the exactcontrolability of linear time-dependentequations. He chose this particularterminology to emphasise the fact that thefeasibility of such controlability is relatedin an essential way to the uniqueness of thesolution to the adjoint problem, typicallyobtained by the Holmgren or theCarleman theorem.

This lecture was the starting point ofnumerous works by himself and his School.In particular, he began by publishing nofewer than three books on the subject inthe same year: Exact controlability,perturbations and stabilisation of distributedsystems in two volumes (1988) and, withJohn Lagnese, Modelling, analysis, andcontrol of thin plates (1988), which containsan abundance of applications to the theoryof elastic plates. In 1995, he establishedwith Enrique Zuazua the generic characterof the controlability of the three-dimensional Stokes equations: if there isno approximate controlability for a givenopen set, then it is always possible to findanother arbitrarily close open set for whichthis type of controlability holds.

These works constituted yet anothermark of his continuing interest in real-lifeapplications. He also was concerned topropose numerically feasibleapproximation methods. These formedthe theme of an article co-authored withRoland Glowinski an article so long thatits nearly three hundred pages took up twoconsecutive issues of Acta numerica (1994-5).

Even though the last works of Jacques-Louis Lions lay in different areas, theycontinued to be partly influenced by themethodology he had developed forquestions of controlability.

In 1990, he started to express his greatinterest in climatology in El planeta tierra.In this book, which was directly publishedin Spanish, he described in a masterlyfashion and with a remarkably accessiblestyle the most important problems in thisscience, such as modelling, numericalsimulation, sensitivity to initial conditions,etc. His last courses at the Collège deFrance, from 1994 to 1998, were on thesesubjects.

The models found in climatologyinclude complex systems of partialdifferential equations, such as those ofNavier-Stokes and of thermodynamics.But these systems had never been seriouslyanalysed from a mathematical viewpoint,although they had been extensively usedsince the 1960s for numerical simulation inweather forecasting.

In spite of the truly diabolic complexity

(as he was fond of saying) of thecombination of partial differentialequations, boundary conditions,transmission conditions, non-linearities,physical assumptions, etc., that enter thesemodels, Jacques-Louis Lions, together withRoger Temam and Shouhong Wang, wasable to study the existence and uniquenessof solutions, in order to establish theexistence of attractors and to proposenumerical methods. He even succeeded inteaching these works on a blackboard, apedagogical tour de force!

In 1995, he began another series ofworks. With Evariste Sanchez-Palencia hedeveloped the theory of sensitiveproblems, exemplified by the boundaryvalue problems that appear in the theoryof linearly elastic membrane shells. Insuch problems which in a sense constitutethe antithesis of well-posed problems arbitrarily small, yet arbitrarily smooth,changes in the right-hand sides of theequations may induce sudden changes inthe properties of their solutions. It isperhaps no coincidence that the analysis ofsuch problems relies in particular onuniqueness theorems that bearresemblance with those needed in theHUM.

In his last works, Jacques-Louis Lionsreturned to the numerical analysis ofparallel algorithms and domaindecomposition methods, in a long series ofNotes aux Comptes Rendus de lAcadémie desSciences, most often co-authored withOlivier Pironneau and published from1997 to 2001. In fact, these kinds of topicshad been on his mind for a long time: asearly as the 1980s, he had already been anardent advocate of installing a parallelcomputer at INRIA. The main idea inthese Notes is to introduce parallelism inthe continuous problem, rather than in thediscrete one an approach that is in factquite general, since it applies equally wellto any problem that is approximated by aniterative method, such as a fractional stepmethod, a decomposition method intosubproblems in optimisation theory, adomain decomposition method, and soforth.

One can only be impressed by theseimmense works, whether by the quality,diversity, and novelty of the mathematicsused, or by the permanent quest for newapplications that were previously believedto be inaccessible.

Like John von Neumann, whom hedeeply admired, Jacques-Louis Lions was avisionary, who very quickly understoodthat the availability of ever-increasingcomputational power could revolutionisethe modelling of phenomena and therebyimprove our knowledge and mastery of thephysical world, provided however that therequired mathematics was simultaneouslycreated and developed. He admirablycontributed to this latter task.

Jacques-Louis Lions justly receivednumerous honours. Although he alwaysremained modest about them, their list istruly astonishing. He was Commander ofthe French Legion of Honour and GreatOfficer of the French National Order of

Merit, a distinction he received at thehands of President Chirac on 23 February1999. He was a member of twenty-twoforeign academies and Honoris CausaDoctor of nineteen universities.

He also received the most prestigiousprizes and delivered the most covetedlectures. He was in particular awardedthree Prizes by the French Academy ofSciences, the John von Neumann Prize in1986, the Harvey Prize from the Technionin 1991, and the Lagrange Prize at theICIAM meeting in Edinburgh in 1999.Jacques-Louis Lions was proud to have had

the rare honour of having shaken the handof Emperor Akihito, when he received thehighly prestigious Japan Prize in 1991. Itwas the climax of a perfectly andmeticulously organised week that hadparticularly impressed him!

On three occasions he was an invitedspeaker at the International Congress ofMathematicians in 1958, 1970, and 1974.He gave the John von Neumann Lecture atthe SIAM meeting in Boston in 1986, wasplenary speaker at the ICIAM Congress inHamburg and at the SIAM Congress inPhiladelphia in 1995, and held the GalileoChair at the University of Pisa in 1996. Healso had the extremely rare honour for ascientist, especially for a mathematician, ofspeaking before a parliament! As part ofthe celebrations for World MathematicalYear 2000, he delivered an addressentitled Will it ever be possible todescribe, understand, and control theinanimate and animate world by means ofthe languages of mathematics andinformatics? in front of the Cortes, whospecially gathered for the occasion inMadrid on 21 January 2000.

He belonged to the most famousacademies, such as the USSR Academy ofSciences and the American Academy ofArts and Sciences, to which he was electedin 1982 and 1986. In 1996, he wassimultaneously elected to the Royal Societyof the United Kingdom, the NationalAcademy of Sciences of the USA, and theThird World Academy of Sciences. Twoyears later he was elected to the AcademiaSinica of China and the AccademiaNazionale dei Lincei in Rome. ThePontifical Academy of Sciences, to which

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he was elected in 1990, seemed to beparticularly dear to him; it may be less wellknown, but it is an unusually rare honourto become one of its members!

Who was the man behind all theseendeavours? What I knew of himconvinced me that both his human andprofessional qualities were trulyexceptional.

Jacques-Louis Lions wrote abundantly,very rapidly, and with an astonishing ease not only in mathematics, but alsocountless letters, his favourite means ofcommunication. He was a master with thefax, which he used with amazing efficiency!For instance, it was not uncommon foreach of his various collaborators at anygiven time to receive four or five faxes perweek, sometimes with up to thirty pages iftheir contents were mathematical.

Even though he wrote abundantly, heconfessed that he rarely kept track of hismanifold letters, perhaps because he couldrely entirely on his memory, or perhapsbecause he preferred to spare himself aherculean archival task! Let us hope thathis correspondents had the good sense tokeep his letters, which could thus be latercompiled.

By any measure, his abilities wereastounding. For instance, he once told methat it took him only a few weeks to writethe several hundred pages of hisDiplodocus lecture notes, mentionedearlier. Likewise, his indifference to lackof sleep or the most extreme jet-lag, andhis freshness after lengthy flights, werealways a subject of astonishment among histravel companions.

As John Ball put it so well, Jacques-Louis Lions was a man of considerablepersonal magnetism and charm, whosecharisma, brilliance as a teacher, andaccessibility attracted others to work withhim. And indeed, it was obvious thatJacques-Louis Lions had an ample share ofcharisma, even if charisma is not easy todefine in a rigorous manner! He was alsoincredibly open and displayed suchamiable and simple manners that any oneof his current students and collaboratorsfelt that they were at the centre of hisattention.

He was also very brave in the face ofphysical danger and suffering. Even whenthe pain became unbearable, he nevercomplained, keeping on the contrary hiscompassion for others. All those who methim will cherish the memory of his warmpersonality, the vision that he so wellconveyed, and his profound intelligence.

Books by Jacques-Louis LionsLectures on elliptic partial differential equations,Tata Institute, Bombay, 1957.Equations différentielles opérationnelles et problèmesaux limites, Springer-Verlag, 1961.Problèmes aux limites dans les équations auxdérivées partielles, Presses de lUniversité deMontréal, 1962.Méthodes de quasi-réversibilité et applications (withR. Lattès), Dunod, 1967; English translation:Quasi-reversibility methods and applications,American Elsevier, 1969.Contrôle optimal de systèmes gouvernés par des

equations aux dérivées partielles, Dunod, 1968;English translation: Optimal control of systemsgoverned by partial differential equations, Springer-Verlag, 1970.Problèmes aux limites non homogènes et applications(with E. Magenes), 3 vols., Dunod, 1968-70;English translation: Non-homogeneous boundaryvalue problems and applications, Springer-Verlag,1972-3.Quelques méthodes de résolution des problèmes auxlimites nonlinéaires, Dunod, 1969.Les inéquations en mécanique et en physique (withG. Duvaut), Dunod, 1972; English translation:Inequalities in mechanics and physics, Springer-Verlag, 1976.Some aspects of the optimal control of distributedparameter systems, CBMS Conference 6, SIAM,1972.Sur le contrôle optimal des systèmes distribués,Monographie 20, EnseignementMathématique, 1973.Perturbations singulières dans les problèmes auxlimites et en contrôle optimal, Lecture Notes inMathematics 323, Springer-Verlag, 1973.Analyse numérique des inéquations variationnelles(with R. Glowinski and R. Trémolières), 2 vols.,Dunod, 1976.Numerical analysis of variational inequalities,North-Holland, 1981.Sur quelques questions danalyse, de mécanique et decontrôle optimal, Presses de lUniversité deMontréal, 1976.Applications des inéquations variationnelles aucontrôle stochastique (with A. Bensoussan),Dunod, 1978.Asymptotic analysis for periodic structures (with A.Bensoussan and G. Papanicolaou), North-Holland, 1978.Some methods in the mathematical analysis of systemsand their control, Science Press, Beijing andGordon & Breach, 1981.Applications of variational inequalities to stochasticcontrol, North-Holland, 1982.Contrôle impulsionnel et inéquations variationnelles(with A. Bensoussan), Gauthier-Villars, 1982.Impulse control and variational inequalities,Heyden & Son, 1984.Contrôle des systèmes distribués singuliers,Gauthier-Villars, 1983.Analyse mathématique et calcul numérique pour lessciences et les techniques (with R. Dautray), 3 vols.,Masson, 1984-8.Mathematical analysis and numerical methods forscience and technology, 9 vols., Springer-Verlag,1988-93.Contrôlabilité exacte, perturbations et stabilisation desystèmes distribués, 2 vols., Masson, 1988.Modelling, analysis and control of thin plates (withJ. Lagnese), Masson, 1988.El planeta tierra, Instituto de España, Espasa-Calpe, 1990.Sentinelles pour les systèmes distribués à donnéesincomplètes, Masson, 1992.Models for the coupled atmosphere and ocean (withR. Temam and S. Wang), ComputationalMechanics Advances 1, North-Holland,Amsterdam, 1993.

Series edited by Jacques-Louis LionsNonlinear partial differential equations and theirapplications, Collège de France Seminar (withH. Brezis), 12 vols., Pitman-Longman, 1981-94.Mathématiques appliquées pour la maîtrise (with P.G. Ciarlet), 21 vols., Masson, 1982-97.Recherches en mathématiques appliquées (with P. G.

Ciarlet), 42 vols., Masson, 1985-97.Handbook of numerical analysis (with P. G.Ciarlet), 7 vols., North-Holland, 1990-2000.Nonlinear partial differential equations and theirapplications, Collège de France seminar (with D.Cioranescu), 2 vols., Pitman, 1998-2001.

Books dedicated to Jacques-Louis LionsAnalyse mathématique et applications,Contributions en lhonneur de Jacques-LouisLions, Gauthier-Villars, 1988.Frontiers in pure and applied mathematics, Acollection of papers dedicated to Jacques-LouisLions on the occasion of his sixtieth birthday(ed. R. Dautray), North-Holland, 1991.Equations aux dérivées partielles et applications,Articles dédiés à Jacques-Louis Lions,Gauthier-Villars, 1998.

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Olga ArsienevkaOleinik

Professor Olga Arsienevna Oleinikpassed away on 11 October at the age of76. She made her mark throughhoutthe world with her articles (almost threehundred!) and her monographs. Afterhaving completed her thesis under theguidance of Professor Petrovski, shebegan her career in the Moscow StateUniversity. She became professor in thesame university, and for a long periodwas held the Chair of DifferentialEquations. She has guided muchresearch, was the adviser of more thanfifty mathematicians, some twenty ofwhom obtained the degree of Doctor ofScience. The range of interests ofProfessor Oleinik was very wide, fromthe study of real analytic manifolds (inconnection with Hilberts sixteenthproblem) to the questions of existenceand uniqueness of solutions of linearand non-linear partial differentialequations.

She is the originator of very generaland elegant proofs of Korns inequality,an essential tool in the theory ofelasticity. She gave talks at numerousinternational congresses and seminars inuniversities throughout the world. Shewas a member of the Russian Academyof Sciences and other academies, andwas also a Doctor Honoris Causa of manyforeign universities. Professor Oleinikwas awarded the medal of the Collège deFrance. J. Leray and J.-L. Lions invitedher several times to this eminentinstitution, since some of her work wasrelated to that of those two distinguishedmathematicians.

She will also remembered as a ladywith a very strong personality. She wasvery generous with her colleagues, andher friendship, once acquired, waslimitless. Her loss will be deeply felt bythe international mathematicalcommunity.

Mireille Chaleyat-Maurel, Université Pierreet Marie Curie, Laboratoire de Probabilités,16, rue Clisson et 175/179 rue du ChevaleretBureau 4D16, 75013 Paris (France)

The Ukrainian Mathematical Congresswas held in Kiev on 21-23 August 2001.It was dedicated to the 200thanniversary of the birth of M.V.Ostrohradsky, a prominent Ukrainianmathematician.

The Congress was organised by theInstitute of Mathematics of the NationalAcademy of Sciences of Ukraine, underthe auspices of the National Academy ofSciences of Ukraine, the Ministry ofEducation and Science of Ukraine, theInstitute of Applied Mathematics andMechanics of the National Academy ofSciences of Ukraine, T. ShevchenkoKiev National University,M. Drahomanov National PedagogicUniversity, the Ukrainian CharitableFoundation for FurtheringDevelopment of Mathematical Science,the Ukrtelecom joint-stock company,and Kiev City State Administration.

This event became the first attempt togather at one major scientific meetingall the scientists of Ukraine that work inmathematics and related fields, thusmaking it possible to assess thecontemporary state of this importantscientific direction and prospects for itsfurther development in Ukraine.

Within the framework of theCongress, twelve satellite internationalscientific conferences were held indifferent fields of contemporarymathematics.

The work of the Congress proceededin thirteen parallel sections in the mainfields of mathematics: Algebra and theory of numbers (Chair:A.V. Roiter) Dynamical systems (Chair:O.M. Sharkovsky) Differential equations and non-linearoscillations (Chair: A.M. Samoilenko) Complex analysis and potential theory(Chair: P.M. Tamrazov) Mathematical physics (Co-Chairs:A.H. Nikitin and D.Ya. Petryna) Teaching methods and history ofmathematics (Co-Chairs:O.M. Bogolyubov, M.I. Shkil andM.I. Yadrenko) Non-linear analysis (Chair:I.V. Skrypnik) Computational mathematics andmathematical problems of mechanics (Co-Chairs: V.M. Koshlyakov,I.O. Lukovsky, V.L. Makarov andI.V. Serhienko)Probability theory and mathematicalstatistics (Co-Chairs: V.S. Korolyuk andM.I. Portenko)Theory of approximations and harmonicanalysis (Co-Chairs: M.P. Korneichukand O.I. Stepanets) Theory of operators and differentialoperator equations (Co-Chairs:Yu.M. Berezansky and

M.L. Horbachuk)Topology and geometry (Co-Chairs:O.A. Borisenko and V.V. Sharko)Mathematical theory of control (Co-Chairs: M.Z. Zhurovsky, V.S. Melnykand A.A. Chykrii)

Section sessions were held at theInstitute of Mathematics of the NationalAcademy of Sciences of Ukraine andM. Drahomanov National PedagogicUniversity.

385 scientists participated in sectionsessions. Among them were 82 foreignmathematicians (52 from the CIS and30 from other foreign countries). Inall, scientists from 27 countriesparticipated in the sessions; thegreatest number of foreign participantscame from Russia, USA, Germany,Italy, Byelorussia and Uzbekistan. Intotal, more than 1500 scientists from 40countries (including about 260 from theCIS and 160 from other foreigncountries) participated in the UkrainianMathematical Congress and satelliteconferences. Below, we present the listof satellite conferences.10-17 June: Stochastic Analysis and itsApplications (Lviv)2-8 July: Third International AlgebraicConference in Ukraine (Sumy) 9-15 July: Fourth InternationalConference on Symmetry in Non-linearMathematical Physics (Institute ofMathematics, National Academy ofSciences of Ukraine, Kyiv)7-12 August: International Conference onComplex Analysis and Potential Theory(Kyiv)13-17 August: Theory of Functions andMathematical Physics (Kharkiv)22-26 August: International Conferenceon Functional Analysis (Institute ofMathematics, National Academy ofSciences of Ukraine, Kyiv)22-28 August: XV InternationalConference on Non-linear PartialDifferential Equations NPDE-2001 (Kyiv) 27-29 August: Differential Equations andNon-linear Oscillations (Chernivtsi) 27-29 August: ComputationalMathematics and Mathematical Problems ofMechanics (Drohobych)27-29 August: International AlgebraicConference (Uzhhorod)11-14 September: Fourth InternationalConference on Geometry and Topology(Cherkasy)1-5 October: New Approaches to theSolution of Differential Equations(Drohobych)

In view of the large number oflectures delivered at the Congress, wemention only well-knownmathematicians and thoserepresentatives of the UkrainianParliament and Government who made

greeting speeches at the openingceremony of the Congress:I.R. Yukhnovsky, Head of theCommittee on Science and Education atthe Ukrainian Parliament, academicianof the National Academy of Sciences ofUkraine (on behalf of the UkrainianParliament); Ya.S. Yatskiv, First DeputyMinister of Education and Science ofUkraine, academician of the NationalAcademy of Sciences of Ukraine (onbehalf of the Ministry of Education andScience of Ukraine); S.O. Dovhyi, Headof the Ukrainian State Committee onCommunications and Information (onbehalf of the Ukrainian Government);I.V. Skrypnik, Academician-Secretary ofthe Department of Mathematics andacademician of the National Academyof Sciences of Ukraine (on behalf of theUkrainian Mathematical Society andthe Department of Mathematics of theNational Academy of Sciences ofUkraine); Rolf Jeltsch, EMS President(on behalf of the EuropeanMathematical Society); BlagovestSendov, academician of the BulgarianAcademy of Sciences, foreign memberof the National Academy of Sciences ofUkraine (on behalf of the BulgarianAcademy of Sciences); W. Wendland(Stuttgart); Nguyen Van Dao (Vietnam),President of the Hanoi NationalUniversity, foreign member of theNational Academy of Sciences ofUkraine; M.M. Lavrentev (Russia),Director of the Institute of Mathematicsof the Siberian Division of the RussianAcademy of Sciences, academician ofthe Russian Academy of Sciences;D. Matarazzo (Italy); RomanAndrushkiv (USA), Deputy President ofthe T. Shevchenko Scientific Society;V.G. Baryakhtar, member of thePresidium of the National Academy ofSciences of Ukraine, academician of theNational Academy of Sciences ofUkraine; V.O. Marchenko, academicianof the National Academy of Sciences ofUkraine; Yu.O. Mitropolsky, HonoraryDirector of the Institute of Mathematicsof the National Academy of Sciences ofUkraine, member of the Presidium ofthe National Academy of Sciences ofUkraine, academician of the NationalAcademy of Sciences of Ukraine;V.V. Petryshyn (USA), foreign memberof the National Academy of Sciences ofUkraine; M.I. Shkil, Rector of theM. Drahomanov National PedagogicUniversity, academician of the Academyof Pedagogic Sciences. Anatoly M. Samoilenko was Head of theOrganising Committee of UMC-2001, isPresident of the Ukrainian Mathematical Societyand is an Academician of the National Academyof Sciences of Ukraine.

SOCIETIES

EMS December 200126

Ukranian Mathematical CongrUkranian Mathematical Congress (UMC-2001)ess (UMC-2001)Anatoly M. Samoilenko

Opening speech by Rolf Jeltsch, EMS

President at the Ukranian

Mathematical CongressLet me thank the organisers and Prof.Skrypnyk for the invitation and the verywarm welcome. I am very happy that Iam allowed to represent the EuropeanMathematical Society at this importantConference. I read though theprogramme this morning and was veryimpressed by the richness of thepresentations, with almost 400 lectures.Let me take the opportunity to tell you alittle bit about the EuropeanMathematical Society. The EMS wasfounded in 1990. It has a doublestructure, in the sense that it is a societyof societies, but also of individualmembers.

It consists of about 50 member societiescovering all of Europe, from Iceland toGeorgia and from Norway to Israel andPortugal at the southern end. Subject-wise we cover all of mathematics, pureand applied, up to and includingindustrial applications.

It may not be known to you that youcan use your reviewing of articles for theZentralblatt to become an individualmember. Members receive our Newsletterevery three months.

What are our scientific activities? Thelargest is of course the EuropeanCongress of Mathematics. We arealready working hard together ourSwedish colleagues on the 2004 congressin Stockholm. I know that our colleaguesfrom Sweden will seek funds to supportparticipants from Eastern Europe.During these congresses the EMS givesten prizes to young mathematicians in allfields, and the Felix Klein Prize for anapplication in industry.

For young researchers we organise twosummer schools every year. This year wehad one in St Petersburg, and one inPrague; its topic is the simulation of fluidand body interaction. Next yearssummer schools will be in Israel onComputational algebraic geometry andapplications, and in Romania in fluidmechanics. At the beginning ofSeptember, EMS is co-organising a largeConference in applied mathematics withSIAM, the Society for Industrial andApplied Mathematics.

Before I move to other activities let metell you that you can find a lot ofinformation about the EMS on our webpage, http://www.emis.de In particular youwill find the address of the committee tosupport Eastern Europeans to attendconferences. Unfortunately the EMS isfinancially weak and hence these fundsare very limited.

Currently the EMS is setting up apublishing house. The managingdirector will be Dr. Hintermann and he

will start in two weeks. The idea is tooffer existing journals to move fromexpensive commercial publishers to ournon-profit organisation.

In addition to these activities we workon a political level in the EuropeanUnion. We try to make the scientificprogrammes of the EU more usable formathematicians. For example, for you itwill be of interest that up to now onecould not support Ukrainian participantsat conferences from EU money. However,we have been able to push that this will bechanged in the 6th Frameworkprogramme which starts in 2003.Moreover, it looks like the handling offunds will be easier too.

Great changes are also happening on

the educational level, starting with theBologna declaration of 1999, which hasbeen signed by 29 European Ministers ofEducation. They want to introduce acommon framework for comparabledegrees, following the concept of abachelor and a masters degree. Clearlythis change will have a great impact.

Let me end with the remark that theEMS is happy to see the strong activitiesof the Ukrainian mathematicalcommunity and its Mathematical Societyin all of mathematics, pure and applied,and not to forget the important teachingof mathematics. This congress is theshowpiece for these activities. I am sureyou all will enjoy the lectures, as I will.Thank you for your attention.

SOCIETIES

EMS December 2001 27

The life and scientific work ofM. V. Ostrogradsky (born 1801)

Mykhailo Vasyliovych Ostrogradsky wasborn in Pashenna village (nowPashenivka) in Poltava region on 24September 1801. His father and mothercame from the Cossack families ofOstrogradsky and Sakhno-Ustimovich,well known since the 17th century. Hestudied at the Poltava gymnasium andthe Kharkiv University (Department ofPhysics and Mathematics), from whichhe graduated with distinction in 1820although did not get the diplomabecause of the intrigues of thereactionary officialdom that ruled in theuniversity at that time. From 1822 to1828 he continued his education inParis, where he obtained significantscientific results.

Ostrogradskys first scientific work, Thetheory of waves in a vessel of cylindrical form(written in the jail, for not having paidthe apartment rent) was approved andpublished by the Paris Academy, and hewas proposed a position in the LycéeHenri IV.

By the time Ostrogradsky came back toRussia, he was already a famous scientist.From 1828 he worked as a professor inthe officer classes of the Naval College,followed by the CommunicationsEngineering Institute (from 1832), theCentral Engineering College (from1840) and the Central Artillery College(from 1841).

He spent the summer holidays inPashenna village working on hisresearch. He died in Poltava on 1January 1962 and, according to his will,was buried in Pashenna village, in hisfamilys sepulchre.

M. V. Ostrogradsky occupies one ofthe most prominent places in the historyof mathematical science. Extraordinarytalent, a bold and brilliant mind, highmathematical erudition, and a goodknowledge of the contemporary naturalsciences permitted him to obtain results

of great importance in many branches ofmathematics and mechanics.

Ostrogradskys scientific work wascarried out during the first half of the19th century, the period whenmathematicians tremendously extendedthe scope of applications of theirresearch, due to the success of thenatural sciences. His research, too, wasdirected chiefly to the study of generallaws of nature.

In his first work on the theory of heat,submitted to the St Petersburg Academyof Sciences in 1928, the young scientisthad already proved the formula thatconnects the integral over a volume andthe integral over the surface (theOstrogradsky-Gauss formula). He wasthe first who understood the role of thisformula and emphasised its importancethroughout mathematics. One of themain achievements of this work is aformulation of the expansion of afunction as a series in eigenfunctions of adifferential operator, and this becamethe central problem in analysis for thewhole century.

His work A memoir on calculatingvariations of multiple integrals, submittedto the St Petersburg Academy of Sciencesin 1834, attracted a great deal ofattention by contemporarymathematicians. The results obtained inthis memoir laid foundations for theintegral calculus of functions of manyvariables. These have long since becomeclassical and are now the main tool in thetheory of partial differential equationsand the calculus of variations.

His series of works on the theory ofintegration of algebraic functions was asignificant contribution to the theory ofalgebraic functions started by Abel,Gauss and Jacobi and, together withLiouvilles works, had a significantinfluence on the subsequentdevelopment of the theory.

In addition to the above-mentionedworks that contained a programme forhis research, Ostrogradsky has manyworks related to the direct integration ofconcrete problems of mathematicalphysics, as well as to problems in algebra,special functions, geometry, probabilitytheory and the calculation of integrals.Many theorems and formulas obtained byhim became part of the standardcurriculum in analysis and differentialequations, although his name is notalways mentioned.

A significant part of Ostrogradskysworks deals with analytical mechanics.He was fortunate to find, independentlyof the Irish scientist Hamilton, one of thefundamental principles in mechanics, theprinciple of least action, and to obtain ageneralised dynamics equation that hasnumerous applications in modernphysics, for studying the motion ofparticles, astronomy, etc. Not only didhe solve many important generalproblems, he also found solutions ofimportant particular problems inhydrostatics, hydrodynamics, elasticitytheory, gravitation theory, ballistics, thetheory of shocks and celestial mechanics.He is the author of fundamental materialin celestial and analytic mechanics.

M. V. Ostrogradsky contributed to thedevelopment of the mathematical culturein Russia, so much so that it cannot beoverestimated. He founded a school ofRussian mathematicians who worked inmechanics and applied mathematics.Being a Full Member of the St PetersburgAcademy of Sciences, Ostrogradsky wasvery popular as a lecturer. His publiclectures helped to promote high ideas ofscience among Russian intellectuals, andin particular to extend the achievementsof the French scientific school which wasat the centre, at that time, of themathematical ideas in which he was mostinterested. The French scientistsCauchy, Laplace, Poisson, Lamé, Poinsotand others had a very high opinion ofOstrogradskys works. He was elected acorresponding member of the ParisAcademy of Sciences, and a full memberof the Rome, Turin and Americanacademies.

There were many prominent scientistsamong Ostrogradskys students: I. O.Vyshnegradsky, founder of automaticcontrol theory; M. P. Petrov, founder ofthe theory of hydrodynamic friction, D. I.Zhuravsky, founder of the theory ofcalculations in bridge construction, andothers. He wrote a number of textbooksand manuals. He also developed a finesystem of teaching methodology, and heinfluenced publishing in Russia, in themiddle of the 19th century, a number oftextbooks that advocated progressivemethods in teaching.

The ideas that come from the works ofM. V. Ostrogradsky are topical in ourtime, too. They find new applications,first of all, in mathematical physics andtheoretical physics, and in other branchesof modern science.

ICIAM 2003Update

from the Congress Director

October 2001In previous updates, I described the processes for choosing the invited speakers forICIAM 2003. Vitally important in this was the excellent work by the InternationalProgram Committee, ably chaired by Professor Ian Sloan.

We now take great pleasure in announcing the following 27 invited speakers for ICIAM2003:

Brian Anderson, Australia (systems, control and signal processing)Marsha Berger, USA (mesh generation, CFD, scientific computing)Yann Brenier, France (non-linear PDE)Franco Brezzi, Italy (finite element methods, engineering applications)Jennifer Tour Chayes, USA (statistical physics, Microsoft theory group)Mark Davis, UK (financial mathematics)James Demmel, USA (numerical linear algebra, simulation)Peter Deuflhard, Germany (modelling, simulation, optimisation)David Donoho, USA (mathematical statistics, wavelets, visualisation)Yoshikazu Giga, Japan (Navier-Stokes, non-linear PDE)Alice Guionnet, France (random interactions, probability, particle

methods)Tom Hou, USA (multiscale and free boundary problems)Jonathan Keating, UK (dynamical systems, asymptotics, quantum chaos)Rupert Klein, Germany (CFD, modelling, combustion)Nancy Kopell, USA (dynamics of the nervous system, mathematical

biology)Tom Leighton, USA (computer science, parallel algorithms, the net)Peter A. Markowich, Austria (semiconductors, kinetics, modelling)Alexander Mielke, Germany (non-linear PDE, dynamics, continuum mechanics)Harald Niederreiter, Singapore (quasi-Monte Carlo methods, discrete

mathematics)Michael Ortiz, USA (solid mechanics, materials)George Papanicolaou, USA (waves, diffusion, multi-scale phenomena)Neil Sloane, USA (error correcting codes, integer sequences)Philippe Toint, Belgium (non-linear optimisation)Ernie Tuck, Australia (ship hydrodynamics, applied fluids)Henk van der Vorst, Netherlands (numerical linear algebra, iterative methods)Ying Lung-an, China (non-linear PDE, numerical methods)Vladimir Zakharov, Russia/USA (turbulence, integrable systems, kinetics)

Our webmaster, Dr Ross Moore, has constructed a lively and colourful page for eachspeaker and you are cordially invited to visit for an inspection. We hope you will agreethe slate of speakers is an outstanding representation of modern industrial and appliedmathematics.

Recent events in the USA might have raised doubts about the attractiveness of air travelto Australia. On that score, Id like to reassure readers that Australia is a vibrantmulticultural country in which peoples from approximately 150 countries liveharmoniously. Australia has a long and cherished democratic tradition; indeed we arecurrently celebrating our 100 years of federation as a democratic nation. Terrorism ismore remote to Australia than to most developed countries. Moreover, the localairlines have an excellent safety record.

It is now time to start making concrete plans to attend ICIAM 2003. If you wish tomake some form of a presentation, then the principal vehicles to do this will beminisymposia, contributed presentations and poster presentations. Some details arealready displayed on the web site www.iciam.org, and others will be added as deadlinesand procedures become clearer.

But now is the time to make your plans. We look forward to giving you a warm Aussiewelcome in July 2003.

Dr Noel BartonCongress Director

EMS December 200128

Please e-mail announcements of Europeanconferences, workshops and mathematicalmeetings of interest to EMS members, tok.a.s.quinn@open.ac.uk. Announcements shouldbe written in a style similar to those here, andsent as Microsoft Word files or as text files (butnot as TeX input files). Space permitting, eachannouncement will appear in detail in the nextissue of the Newsletter to go to press, andthereafter will be briefly noted in each new issueuntil the meeting takes place, with a reference tothe issue in which the detailed announcementappeared.

28-1 February: International Conference onFactorization, Singular Operators andRelated Problems, Funchal, Madeira,Portugal[dedicated to the 70th birthday of ProfessorGueorguii Litvinchuk]Programme committee: A. Antonevich(Belarussia), A. Boettcher (Germany), B.Bojarskii (Poland), R. Duduchava (Georgia), M.Kaashoek (Netherlands), N. Karapetiants(Russia), Yu. Karlovich (Mexico), V.Kokilashvili (Georgia), N. Krupnik (Israel), V.Mazya (Sweden), V. Rabinovich (Mexico), B.Silbermann (Germany), I. Simonenko (Russia),I. Spitkovsky (USA), N. Vasilevskii (Mexico)Organising committee: Stefan Samko,Chairman (Algarve), Victor Kravchenko(Algarve), Jose Molarinho Carmo (Madeira),Jose Castanheira da Costa (Madeira), RitaVasconcelos (Madeira), Antonio Ferreira dosSantos (Lisboa), Francisco Teixeira (Lisboa),Amarino B. Lebre (Lisboa), Ana Moura Santos(Lisboa)Information: contact Prof. Dr Stefan Samko,Universidade do Algarve Faculdade de Cienciase Tecnologia, Campus de Gambelas, Faro, 8000,Portugale-mail: ssamko@ualg.ptWeb site: http://www.digiways.com/fsorp/

1-30 April: Special Research Trimester onDynamical Systems, PisaInformation:Web site:http://www.math.sns.it/degiorgi/dynsys/[For details, see EMS Newsletter 41]11-15: Neural Networks and Applications(NNA 02), Interlaken, SwitzerlandInformation:Web site:http://www.worldses.org/wses/calendar.htm11-15: Fuzzy Sets and Fuzzy Systems (FSFS02), Interlaken, SwitzerlandInformation:Web site:http://www.worldses.org/wses/calendar.htm11-15: Evolutionary Computations (EC 02)Interlaken, SwitzerlandInformation:

February 2002

January 2002

Web site:http://www.worldses.org/wses/calendar.htm

18-19: Workshop on Under- and Over-determined Systems of Algebraic andDifferential Equations, Karlsruhe, GermanyInformation:Web site: http://iaks-www.ira.uka.de/iaks-calmet/ ADE[For details, see EMS Newsletter 41]21-22: Eighth Rhine Workshop on ComputerAlgebra, Mannheim, GermanyInformation:Web site: http://www.uni-mannheim.de/RWCA[For details, see EMS Newsletter 41]26-4 April: International Centre forMathematical Sciences EuroSummer Schooland Instructional Conference onCombinatorial Aspects of MathematicalAnalysis, Edinburgh, UKInformation:Web site:www.ma.hw.ac.uk/icms/meetings/2002/camaFebruary 2002[For details, see EMS Newsletter 41]

1-30 June: Trimester on Algebraic Topology,Barcelona, SpainTopics: algebraic topology, especially sometopics in modern homotopy theory, includinghomotopy finite group theory, functor calculusand model category structuresMain visitors: S. Dourlens, J. Greenlees, J.Grodal, N. Kitchloo, R. Levi, J. Moller, D.Notbohm, B. Oliver, P.-E. Parent, N. StricklandLocation: Centre de Recerca Matemàtica,Bellaterra

13-17: 34th Journées de Statistique, Brusselsand Louvain-la-Neuve, BelgiumInformation:Web site: www.stat.ucl.ac.be/JSBL2002[For details, see EMS Newsletter 41]15-17: Fourth International Conference onAdvances in Fluid Mechanics, Ghent,BelgiumAim: to provide a forum for the interchange ofnew ideas and the presentation of the latest workin the field. Work discussed will appear infuture volumes of the book series Advances inFluid Mechanics, the Editorial Board of whichserves as the scientific advisory committee forthe conference. The basic mathematicalformulations of fluid mechanics and theircomputer modelling will be discussed, as well asthe relationship between experimental andanalytical resultsTopics: experimental versus simulationmethods, numerical methods in fluid mechanics,boundary element methods, fluid-structureinteraction, convection, heat and mass transfer,

May 2002

April 2002

March 2002

hydrodynamics, coastal sea modelling, river,lake and estuary dynamics, wave modelling,multi-phase flow, acoustics, environmental fluidmechanics, high-performance computing in fluidmechanics, bio-fluids, material properties andfluids, industrial applicationsCall for papers: papers are invited on the topicsoutlined and others falling within the scope ofthe meeting. Abstracts of no more than 300words should be submitted to the conferencesecretariat, and should clearly state the purpose,results and conclusions of the work to bedescribed in the final paper. Final acceptancewill be based on the full-length paper, which ifaccepted, must be presented at the conference.Each submitted paper is subject to a separateregistrationProgramme committee: C.A. Brebbia (UK),M. Rahman (Canada), R. Verhoeven (Belgium) Organising committee: A. Chakrabarti (India),G. Comini (Italy), L. Debnath (Florida), J.P. duPlessis (South Africa), M.M. El-Refaee(Kuwait), R.C. Gupta (Singapore), D.B. Ingham(Leeds), A. Jeffrey (Newcastle-upon-Tyne), A.Mendes (UK), T.B. Moodie (Canada), M.A.Noor (Canada), W. Perrie (Canada), H. Pina(Portugal), D. Prandle (UK), M.G. Satish(Canada), P. Skerget (Slovenia), P.A. Tyvand(Norway), L.C. Wrobel (Brunel)Organisers: Wessex Institute of Technologyand University of Ghent, BelgiumProceedings: will be published in hard coverbook form by WIT Press; available to delegatesat the time of registration and widely distributedafter the conference through the internationalbook trade. Further details can be found atwww.witpress.comLocation: the Cultural Centre of the GhentUniversity Het PAND, a former Dominicanmonastery, located in the historical center of thecity, on the banks of the river LeieDeadlines: for abstracts, as soon as possible; forpapers, 18 December Information: contact Stacey Hobbs, ConferenceSecretariat, AFM 2002, Wessex Institute ofTechnology, Ashurst Lodge, AshurstSouthampton SO40 7AA, UK, tel: 44 (0) 238 029 3223, fax: 44 (0) 238 0292853e-mail: shobbs@wessex.ac.ukWeb site: http://www.wessex.ac.uk/conferences/2002/afm02/index.html19-26: Symmetry and Perturbation Theory(SPT2002), Cala Gonone, Sardinia, ItalyOrganisers: S. Abenda (Bologna), G. Gaeta(Milano and Roma), S. Walcher (Munich)Information:Web site:http://web.tiscalinet.it/spt_spt/spt2002.html22-24: Discrete Groups and GeometricStructures, with Applications(Crystallographic Groups and theirGeneralizations III), Kortrijk, BelgiumMain speakers: Y. Benoist (Paris), B. Farb(Chicago), D. Fried (Boston), F. Labourie(Orsay), A. Lubotzky (Jerusalem, to beconfirmed), G. Soifer (Bar Ilan), R. Grigorchuk(Moscow)Topics: recent developments concerninginteractions between group theory and geometry,including geometric group theory, group actionson manifolds, crystallographic groups andgeneralisations (affine, polynomial, almost-crystallographic), discrete subgroups of Liegroups, graphs of groups; applications in and

CONFERENCES

EMS December 2001 29

FForthcoming conferorthcoming conferencesencesCompiled by Kathleen Quinn

beyond the fields mentionedProgramme committee: H. Abels (Bielefeld),Y. Felix (Louvain-la-Neuve), W. Goldman(College Park), F. Grunewald (Duesseldorf), P.Igodt (Leuven/Kortrijk), K.B. Lee (Norman,Oklahoma)Organising committee: K. Dekimpe, P. Igodt,W. Malfait (all at Kortrijk), Y. Felix (Louvain-la-Neuve)Programme: short communications and postersAbstracts: should be sent toPaul.Igodt@kulak.ac.beSponsors: K.U. Leuven Campus Kortrijk, Fundfor Scientific Research Flanders (Belgium),F.W.O. Scientific Research NetworkFundamental methods and techniques inmathematicsLocation: K.U. Leuven CampusInformation:e-mail: workshop@kulak.ac.beWeb site: http://www.kulak.ac.be/workshop25-3: XXII International Seminar on StabilityProblems for Stochastic Models (SPSM) andSeminar on Statistical Data Analysis (SDA),Varna, BulgariaInformation:Web site: http://stabil.fmi.uni-sofia.bg[For details, see EMS Newsletter 41]27-29: Spring School on Frobenius Manifoldsin Mathematical Physics, Enschede, TheNetherlandsInformation:e-mail: nijpjes@sci.kun.nl27-31: 6th Congress of SIMAI (Italian

Society for Applied and IndustrialMathematics), Chia, Island of Sardinia, ItalyScope: applied mathematics and the applicationsof mathematics in technology, finance,medicine, environment and societyMain speakers: U. Barberis (Genoa), H.Berestycki (Paris), A. Murli (Naples), H.Ockendon (Oxford), R. Rannacher (Heidelberg)Languages: English and ItalianAbstracts: in English, up to a maximum of 4pages, should be sent tosimai2002@iac.rm.cnr.it, indicating the type ofpresentation (invited, oral or poster; mini-symposium or focus session) in the subject lineof the e-mail. The volume of abstracts and theCongress programme will be distributed at theregistration desk. The format (Latex or Word)for the preparation of the abstracts can bedownloaded fromhttp://www.iac.rm.cnr.it/simai, by clicking onsimai 2002Programme committee: U. Barberis (Genoa),V. Boffi (Rome), F. Brezzi (Pavia), E. DeBernardis (Rome), G. Fotia (Cagliari), N.Gomiero (Marano Ticino, NO), M. Primicerio(Florence; President), L. Puccio (Messina), V.Valente (Rome)Organising committee: V. Boffi (Rome;President), N. Dessi (Cagliari), G. Fotia(Cagliari), M. Gaviano (Cagliari), F. Maggio(Cagliari), S. Seatzu (Cagliari; Vice-President),V. Valente (Rome)Location: Congress Center at the Grand HotelChia, LagunaDeadlines: for proposals of mini-symposia,focus sessions and round tables, 15 December;for all presentations (oral and postercommunications; communications in the frameof mini-symposia and focus sessions; contentsof round tables; invited lectures), 28 February Information: contact organising secretariat: G.

Castellini, SIMAI, c/o IAC/CNR - Viale delPoliclinico, 137 - I-00161 Rome; tel. +39-06-88470213; fax +39-06-4404306; e-mail:castellini@iac.rm.cnr.it; or P. Rughetti,IAC/CNR - Viale del Policlinico, 137 - I-00161Rome, tel. +39-06-88470249; fax +39-06-4404306; e-mail: rughetti@iac.rm.cnr.itWeb site: http://www.iac.rm.cnr.it/simai (clickon simai 2002)28-31: 2nd International Conference onAdvanced Computational Methods inEngineering (ACOMEN 2002), Liège,BelgiumTheme: advanced numerical and computationalmethods, such as (adaptive) finite element, finitevolume and finite difference methods, boundaryelement methods, spectral methods and domaindecomposition techniques, applied to direct andinverse problems in the following themes: solidand structural mechanics, acoustics andvibration control, heat/mass transfer and phasechange, environmental engineering, fluid flowand porous media, electric and magnetic fields,industrial topics, computational mathematicsand simulationAim: to act as a forum for engineers and appliedmathematicians, dealing with advancednumerical strategies, computational methods andsimulation in various engineering disciplinesInvited speakers: C. Beckermann (Iowa), T.Belytschko (Illinois), A. Bossavit (France), M.Géradin (Belgium), K. Morgan (Wales), E.Onate (Spain, president of ECCOMAS), H. VanBrussel (Belgium), H. Van Duijn (Netherlands)Organising committee: M. Hogge (Liège), H.De Schepper (Ghent), R. Van Keer (Ghent), E.Noldus (Ghent)Location: Campus Sart Tilman, LiègeUniversityInformation:e-mail: acomen@cage.rug.ac.beWeb site: http://cage.rug.ac.be/~acomen

4-13: 3rd Linear Algebra Workshop BLED2002, Bled, SloveniaInformation:Web site: http://www.ijp.si/ftp/pub/STOp/law/[For details, see EMS Newsletter 41]5-9: Conference in Honour of Hans Wallin,Umea, SwedenInformation: Web site: http://www.math.umu.se/aktuellt/HWkonferens.htm[For details, see EMS Newsletter 41]6-15: Fourth International Conference onGeometry, Integrability and Quantization,Varna, BulgariaAim: to bring together experts in classical andmodern differential geometry, complex analysis,mathematical physics and related fields, toassess recent developments in these areas and tostimulate research in related topicsMain speakers: A. Calini (curve geometry andsoliton theory), G. Naber (equivariantlocalisation: exactness of the stationary phaseapproximation), R. Schmid (diffeomorphism,gauge and loop groups, Lie groups ofpseudodifferential and Fourier integraloperators), W. Zakrzewski (geometry of sigmamodels, to be confirmed)Organising committee: Ivailo M. Mladenov(Sofia), Gregory L. Naber (Chico)Advisory committee: P. Exner (Praha), M. de

June 2002

Gosson (Karlskrona), T. Iwai (Kyoto), R. Picken(Lisboa) and I. Vaisman (Haifa) International Standing Committee: B.Konopelchenko (Lecce), M. de Leon (Madrid),A. Odzijewicz (Bialystok), H. Sato (Nagoya)and W. Schempp (Siegen)Sponsors: Bulgarian Academy of Sciences,California State University Chico, EuropeanMathematical SocietyProceedings: to be published by aninternationally recognised scientific publisher.Proceedings of previous conferences can befound at http://coral.dir.bg/geom.htmFees: a nominal registration fee of $150 if paidthrough a bank transfer up to 31 March; thiscovers a copy of the proceedings and theorganised activities. Later registration paiddirectly upon arrival is $200Information:e-mail: MLADENOV@BGCICT.ACAD.BG,GNABER@CSUCHICO.EDUWeb site: http://www.bio21.bas.bg/conference/10-16: Aarhus Topology 2002, Aarhus,DenmarkInformation:Web site: http://www.imf.au.dk/AT2002/[For details, see EMS Newsletter 41]11-13: Third International Symposium onRemote Sensing of Urban Areas, Istanbul,TurkeyTopics: new observation sensors (systems) forurban monitoring, high spatial resolutionsatellite sensor data for urban applications,digital photogrammetric applications in urbanareas, monitoring urban growth (trend analysis,change detection), differentiation of the innerparts of cities, creating urban digital elevationmodels, GIS/GPS technology for urbanapplications, urban management systems,hydrological/geological assessment of urbanareas, meteorological/ecological assessment ofurban areas, national and international projectsusing remote sensing and GIS, ecological(urban) risk analysis in urban areas using remotesensing, remote sensing and GIS forhistorical/archeological applications, ruralapplications (natural resource managementsystems), using remote sensing and GIS forsustainable urban development, digital/virtualcity models and GIS based traffic management,radar remote sensing of urban areas, thermalinfra-red remote sensing of urban areas, remotesensing of urban vegetation, remote sensing ofcontaminated land in urban areasOrganising committee: Derya Maktav(Istanbul, Chair), Carsten Jürgens (Regensburg,Co-chair), Filiz Sunar Erbek (Istanbul), FaroukEl-Baz (Boston), Garik Gutman (NASA),Manfred Ehlers (Vechta), Ediz Hun (President,Environment Commission, Turkey), OrhanAltan (Istanbul), Hasan Akgün (BüyükçekmeceMunicipality, Turkey), Arnon Karnieli (BenGurion University), Robert Laurini (Lyon)Deadline: for abstract submission, 15 DecemberInformation: contact Prof. Dr. Derya Maktav(Symposium Chair), Istanbul TechnicalUniversity, Department of Remote Sensing; e-mail: dmaktav@ins.itu.edu.tr; CarstenJürgens,(Co-chair), Regensburg University,Department of Geography; e-mail:carsten.juergens@geographie.uni-regensburg.de;or, for general correspondence, inquiries andsubmission of papers, Filiz Sunar Erbek,Ýstanbul Teknik Üniversitesi, Ýnþaat Fakültesi,80626 Maslak, Istanbul, Turkey; tel: 0090-0212-

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2853801; fax:0090-0212-5737027; e-mail:fsunar@srv.ins.itu.edu.trWeb site: http://www.ins.itu.edu.tr/deryamaktav17-19: 24th World Conference on BoundaryElement Methods incorporating MeshlessSolutions Seminar Sintra, PortugalScope: the internationally recognised forum fordisseminating the latest boundary elementmethod and its applications. BEM is a veryactive area of research with the method beingsuccessfully applied to solve difficultengineering and scientific problems. Thisincludes the solution of non-linear and time-dependent problems. Considerable advanceshave also been made in the solution of complexfluid dynamic problems and the use of highperformance computing. The conference willdeal with the topics listed, as well as papers of amore theoretical character. State-of-the-artreviews and advanced mathematical andcomputational aspects will also be discussedSpecial feature: seminar on meshless methods,which will discuss the use of integral equationswithout meshes. Many techniques will behighlighted including, fundamental solutions,Galerkin, diffuse methods, localised collocation,cloud and diffusive methods and modifiedTrefftz techniquesTopics: dynamics and vibrations, fracturemechanics and fatigue, inelastic problems,composite materials, plates and shells, contactmechanics, geomechanics, material processingand metal forming, soil and soil structureproblems, electrostatics and electromagnetics,biomechanics, inverse problems, fluid flow,interfacial and free surface flow, transportproblems, wave propagation problems,acoustics, dual reciprocity method and basisfunctions, fundamental principles, computationaltechniques, advanced formulations, sensitivityanalysis and optimization, meshless methodsseminar, fundamental solution method, source-field superposition, diffuse methods, localmeshless methods, modified Trefftz methods,natural element methods, charge simulationmethods, element-free Galerkin, cloud methods,point collection methodsCall for papers: papers are invited on the topicsoutlined and others falling within the scope ofthe meeting. Abstracts of no more than 300words should be submitted to the conferencesecretariat, and should clearly state the purpose,results and conclusions of the work to bedescribed in the final paper. Final acceptancewill be based on the full-length paper, which ifaccepted, must be presented at the conference.Each submitted paper is subject to a separateregistrationProgramme committee: G. Beer (Austria),M.B. Bush (Australia), C.Y. Cha (USA), C.S.Chen (USA), A.H.-D. Cheng (USA), G. De Mey(Belgium), V. DeGiorgi (USA), N.A. Dumont(Brazil), A. El-Zafrany (UK), L. Gaul(Germany), G.S. Gipson (USA), M.A. Golberg(USA), L. Gray (USA), S. Grilli (USA), K.Hayami (Japan), M.S. Ingber (USA), D.B.Ingham (Leeds), N. Kamiya (Japan), D.LKarabalis (Greece), A.J. Kassab (USA), J.T.Katsikadelis (Greece), E. Kita (Japan), W.J.Mansur (Brazil), S. Mukherjee (USA), K.Onishi (Japan), F. Paris (Spain), H. Power(Nottingham), P. Prochazka (Czech Republic),J.J. Rencis (USA), T.J. Rudolphi (USA), B.Sarler (Slovenia), E. Schnack (Germany), A.P.Selvadurai (Canada), L. Skerget (Slovenia), V.

Sladek (Slovakia), S. Syngellakis(Southampton), Masa Tanaka (Japan), N.Tosaka (Japan), T. Tran-Cong (Australia), W.S.Venturini (Brazil), O. von Estorff (Germany),L.C. Wrobel (Brunel), T. Wu (USA)Organisers: Wessex Institute of Technology,UK and University of Coimbra, PortugalOrganising committee: C.A. Brebbia (UK), A.Tadeu (Portugal), V. Popov (UK)Sponsors: International Society of BoundaryElements (ISBE), International Journal ofEngineering Analysis with Boundary ElementsProceedings: will be published in hard coverbook form by WIT Press; available to delegatesat the time of registration, and widely distributedafter the conference through the internationalbook tradeDeadlines: for abstracts, as soon as possible; forpapers, 15 JanuaryInformation: contact Rachel Green, ConferenceSecretariat, BEM 24, Wessex Institute ofTechnology, Ashurst Lodge, Ashurst,Southampton, SO40 7AA, UK; tel: 44 (0) 238 029 3223; fax: 44 (0) 238 0292853e-mail: rgreen@wessex.ac.ukWeb site: http://www17-21: Seventh International Conference onp-adic Functional Analysis, University ofNijmegen, The NetherlandsScope: analysis over valued fields other than thereal or complex numbers (such as the p-adicnumber field or Krull valued fields). The mainmathematics subject classifications are 46S10,47S10, 32P05, 26E30Scientific committee: W. Schikhof (Nijmegen,Netherlands), A. Escassut (Clermont Ferrand,France), C. Perez-Garcia (Santander, Spain)Speakers (preliminary list): J. Araujo, J.M.Bayod, M. Berz, A. Boutabaa, B. Diarra, A.Escassut, N. De Grande-De Kimpe, L. VanHamme, J. Kakol, A. Katsaras, H. Keller, A.Khrennikov, A. Kochubei, A. Lemin, H.Ochsenius, C. Perez-Garcia, Dinamerico Pombojr, S. Priess, P. Ribenboim, A. Salinier, W.Schikhof, N. Shell, W. Sliwa, S. VegaInformation:e-mail: schikhof@sci.kun.nlWeb site: http://www.sci.kun.nl/math/p-adic2002/17-21: XVth Householder Symposium onNumerical Linear Algebra, Peebles, ScotlandTheme: numerical linear algebraCall for papers: see web siteProgramme committee: N. Higham(Manchester, Chair), A. Bunse-Gerstner(Bremen), T. Chan (Los Angeles), C. Davis(Toronto), D. OLeary (Maryland), M. Overton(Courant Institute), G.W. Stewart (Maryland),H. van der Vorst (Utrecht), P. Van Dooren(Louvain-la-Neuve), C. Van Loan (Cornell)Organising committee: P. Knight (Strathclyde),A. Ramage (Strathclyde), A. Wathen (Oxford)Location: Peebles Hotel Hydro, Peebles,ScotlandGrants: support available for students andothers with limited access to other fundingNotes: the 11th Householder Prize for the bestthesis in numerical algebra written since 1January 1999 will be awarded at the meetingDeadline: for abstracts, 11 December Information:e-mail: alison@maths.strath.ac.ukWeb site:http://www.maths.strath.ac.uk/~matrix/

17-22: School on Population Dynamics,Bedlêwo, PolandScope: organised within the EU ProgrammeCentre of Excellence coordinated by the StefanBanach International Mathematical Centrethrough the Package Mathematical Modellingand Analysis of Cellular PopulationsTheme: mathematical theory and methodsapplied to study populations of entities,including cells, genes, and biomoleculesTopics: adaptive dynamics, ecology,epidemiology, physiology, structuredpopulations dynamicsProgramme: main courses: O. Arino (France),ecology; O. Diekmann, adaptive dynamics; M.Iannelli (Italy), epidemiology; M.C. Mackey(Canada), physiology; G.F. Webb (USA),structured populations dynamics. There willalso be a series of one-hour lectures given bymembers of the scientific committee and 15min. communications by participantsProgramme committee: O. Arino (France), O.Diekmann (The Netherlands), M. Kimmel(USA), A. Lasota (Poland), M.C. Mackey(Canada), P.K. Maini (UK), F. Przytycki (MainCoordinator of the Project of Centre ofExcellence, Poland), R. Rudnicki (Coordinatorof the Package, Poland), Z. Taib (Sweden)Organising committee: T. Kulpa (Poland), K.Pichór (Poland), R. Rudnicki (Chair, Poland),M. Tyran-Kamiñska (Poland)Sponsors: European Commission, Polish StateCommittee for Scientific Research, Institute ofMathematics Polish Academy of Sciences,University of SilesiaLocation: Mathematical Conference Centre, apalace complex in BedlêwoGrants: possible reduction of fee for a limitednumber of participantsDeadlines: for financial support, 20 January; forregistration, 20 AprilInformation:e-mail: cmmpd@ux1.math.us.edu.plWeb site: http://www.math.us.edu.pl/cmmpd/18-22: Barcelona Conference on StochasticInequalities and their Applications(EuroConference), Bellaterra, Barcelona,SpainScientific committee: E. Giné, Ch. Houdré andD. NualartOrganising committee: D. Nualart, F. Utzet, A.Kohatsu and M. JolisInformation:Web site: http://www.crm.es/stochineq24-28: Conference on MathematicalModelling of Population Dynamics, Bêdlewo,PolandScope: organised within the EU ProgrammeCentre of Excellence coordinated by the StefanBanach International Mathematical Centrethrough the Package Mathematical Modellingand Analysis of Cellular PopulationsTopics: the focus will be on mathematicalmodelling and model analysis of populations atvarious levels, including cells, genes,biomolecules and of population dynamics in thefollowing broad themes: ecology, epidemiologyand infectious diseases, evolution, immunologyand cancer growth, physiologyMain speakers: U. An der Heiden (Germany),P. Auger (France), K.-P. Hadeler (Germany), K.Sigmund (Austria), H.R. Thieme (USA). Programme committee: O. Arino (France), O.Diekmann (Netherlands), M. Kimmel (USA), A.Lasota (Poland), M.C. Mackey (Canada), P.K.

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Maini (UK), F. Przytycki (Main Coordinator ofthe Project of Centre of Excellence, Poland), R.Rudnicki (Coordinator of the Package, Poland),Z. Taib (Sweden)Organising committee: T. Kulpa (Poland), K.Pichór (Poland), R. Rudnicki (Chair, Poland),M. Tyran-Kamiñska (Poland)Sponsors: European Commission, Polish StateCommittee for Scientific Research, Institute ofMathematics Polish Academy of Sciences,University of SilesiaProceedings: to be published in Banach CenterPublicationsLocation: Mathematical Conference Centre, apalace complex in BêdlewoGrants: possible reduction of fee for a limitednumber of participants, especially for PhDstudents and young researchersDeadlines: for financial support, 20 January; forregistration, 20 AprilInformation:e-mail: cmmpd@ux1.math.us.edu.plWeb site: http://www.math.us.edu.pl/cmmpd/27- 3 July: Fifth International Conference onCurves and Surfaces, Saint-Malo, FranceInformation:e-mail: saint-malo@imagWeb site: http://www-lmc.imag.fr/saint-malo/

1-6: Advanced Course on MathematicalFinance: Models, Bellaterra, Barcelona,SpainCoordinator: Joan del CastilloInformation:Web site: http://www.crm.es/matfin1-6: 2nd International Conference on theTeaching of Mathematics at UndergraduateLevel, Chersonissos, Crete, GreeceTopics: educational research, technology,innovative teaching methods, curriculainnovations, preparation of teachers,mathematics and other disciplines, distancelearningMain speakers: Hyman Bass (USA), DeborahBall (USA), Jean-Pierre Bourguignon, (France),Miguel De Guzman (Spain), Peter Galbraith(Australia), Oh Nam Kwon (Korea), JoannaMamona-Downs (Greece), Verdiana Masanja(Tanzania), Alan Schoenfeld (USA), ManKeung Siu (Hong Kong, China), David Smith(USA), Tosun Terzioglu (Turkey)Call for papers: abstracts for paper or posterpresentation should be submitted; authors ofproposals accepted for paper presentation maysubmit an article for inclusion in theproceedings. Full papers will be reviewed bymembers of the international programmecommittee. The proceedings will be publishedby J. Wiley Inc. and available at the conference.See below for deadlinesInternational programme committee: I.Vakalis (USA; Chair), D. Hughes-Hallett (USA;Co-chair), Ch. Kourouniotis (Greece; Co-chair),C. Tzanakis (Greece; Co-chair), M. Abboud(Lebanon), A. Arcavi (Israel), H. Arikan(Turkey), M. Artigue (France), G. Baker (USA),E. Barbin (France), W. Barker (USA), J.Belward (Australia), B. Blyth (Australia), R.Borelli (USA), P. Cretchley (Australia), F.Demana (USA), J. Engelbrecht (South Africa),Y. Ersoy (Turkey), V. Farmaki (Greece), F.Furinghetti (Italy), E. Gavosto (USA), A.Gleason (USA), N. Hadjisavvas (Greece), C.

July 2002

Hatzikyriakou (Greece), H-W. Henn (Germany),D. Holton (New Zealand), M. Isoda (Japan), C.Julie (South Africa), F. Kalavassis (Greece), U.Kirchgraber (Switzerland), M. Kourkoulos(Greece), E. Koleza (Greece), B. Kutzler(Austria), Th. Kyriazis (Greece), C. Laborde(France), M. Lambrou (Greece), Ch. Lemonidis(Greece), J. van Maanen (Holland), W.McCallum (USA), M. Majewski (United ArabEmirates), V. Makrakis (Greece), J. Mamona-Downs (Greece), S. Negrepontis (Greece), B.Osgood (USA), P. Pamfilos (Greece), S.Papastavridis (Greece), T. Patronis (Greece), M.Petrakis (Greece), J.D. Phillips (USA), D. Potari(Greece), D. Quinney (UK), A. Radunskaya(USA), Ch. Sakonidis (Greece), G. Schubring(Germany), M-K. Siu (China), J. Uhl (USA), B.Waits (USA), T. Wang (USA), L-P. Yee(Singapore), Th. Zachariades (Greece)Academic sponsors (provisional): BowdoinCollege, Capital University, Duke University,ETH-Zurich, Ewha Womans University,Franklin University, Harvey Mudd College,Middle East Technical University, PomonaCollege, Project Kaleidoscope, StanfordUniversity, Ohio State University, UniversitéParis 7 Denis Diderot, University of Arizona,University of Athens, University of Crete,University of Southern Queensland, John Wileyand Sons Inc.Location: Conference Centre of Knossos RoyalVillage, Hersonissos, Crete, GreeceGrants: probably support for participants fromcountries in a difficult economic situation andyoung mathematiciansDeadlines: for early registration, 31 January; forabstracts, already passed; for full papers 30JanuaryInformation:e-mail: ivakalis@capital.edu,chrisk@math.uoc.gr, tzanakis@edc.uoc.grWeb site: http://www.math.uoc.gr/~ictm22-6: 2002 Barcelona Conference on AlgebraicTopology (EuroConference), Barcelona,SpainScientific committee: C. Broto, C. Casacuberta,H. MillerOrganising committee: J. Aguadé, C.CasacubertaInformation:Web site: http://www.crm.es/2002bcat15-18: Modular Curves and Abelian Varieties(EuroConference), Bellaterra, Barcelona,SpainCoordinator: J. QuerInformation:Web site: http://www.crm.es/mcav0216-22: 7th International Spring School:Nonlinear Analysis, Function Spaces andApplications (NAFSA 7), Prague, CzechRepublicInformation:Web site: http://www.math.cas.cz/~nafsa7[For details, see EMS Newsletter 40]

3-10: Logic Colloquium 2002 (ASL EuropeanSummer Meeting), Münster, GermanyInformation:Web site: http://www.math.uni-muenster.de/LC2002/[For details, see EMS Newsletter 41]5-9: International Conference on Ill-Posedand Inverse Problems, Novosibirsk, Russia

August 2002

[in honour of the 70th anniversary of the birth ofProf. M.M. Lavrentev]Theme: ill-posed problems, inverse problems,tomography and other imaging modalities,numerical analysis and applicationsCall for papers; registration: see web siteProgramme committee: V.G. Romanov (Russia), Yu.E. Anikonov (Russia), M.I.Belishev (Russia), Yu.Ya. Belov (Russia), A.L.Bukhgeim (Russia), G. Chavent (France), D.Colton (USA), A.M. Denisov (Russia), H.W.Engl (Austria), A.M. Fedotov (Russia), Y. Iso(Japan), S.I. Kabanikhin (Russia), O.A.Klimenko (Russia), R. Kress (Germany), M.M.Lavrentev (jr.) (Russia), A. Lorenzi (Italy),B.A. Mair (USA), G.I. Marchuk (Russia), Z.Nashed (USA), V.V. Pickalov (Russia), P.Sabatier (France), O. Scherzer (Germany), S.I.Smagin (Russia), V.N. Strahov (Russia), Y.M.Sultangazin (Kazakhstan), J. Sylvester (USA),G. Uhlmann (USA), V.V. Vasin (Russia), A.G.Yagola (Russia), Sh. Yarmukhamedov(Uzbekistan)Sponsors: Sobolev Institute of Mathematics,Novosibirsk State University, Krasnoyarsk StateUniversity, Russia Foundation for BasicResearchDeadlines: for preregistration, 31 December; forabstracts, 31 MayInformation:e-mail: mml@math.nsc.ruWeb site: www.math.nsc.ru/conference/mml10-11: Colloquium Logicum 2002, Münster,Germany[satellite conference of Logic Colloquium 2002]Information:Web site: http://wwwmath.uni-muenster.de/LC2002/[For details, see EMS Newsletter 41]25-30: Wireless And Optical Communications(WOC 02), Miedzyzdroje, PolandInformation:Web site:http://www.worldses.org/wses/calendar.htm25-30: Nanoelectronics, Nanotechnologies(NN 02), Miedzyzdroje, PolandInformation:Web site:http://www.worldses.org/wses/calendar.htm

3-7: 8th International Conference onStability, Control and Rigid BodiesDynamics, Donetsk, UkraineTheme: problems of general mechanics,stability and control theoriesTopics: stability theory, control in dynamicalsystems, dynamics of rigid body and of multi-body systems, methods of rigid body dynamicsin the theory of elasticityMain speakers: A. Agrachev (Russia), L. Chua(USA), C. Corduneanu (USA), A. Fradkov(Russia), B. Jakubczyk (Poland), W. Respondek(France), V. Rumyantsev (Russia), H. Troger(Austria), S. Vasilyev (Russia)Languages: Ukrainian, Russian, EnglishProgramme: 45-minute invited plenarylectures, 30-minute section lectures, shortpresentations (15-minute communications andposters)Call for papers: abstracts (up to 1 page, inTeX) should be submitted by e-mailProgramme committee: A. Agrachev (Russia),F. Chernousko (Russia), L. Chua (USA), C.

September 2002

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EMS December 200132

Corduneanu (USA), M. Fliess (France), A.Fradkov (Russia), L. Hatvani (Hungary), B.Jakubczyk (Poland), D. Klimov (Russia), V.Kuntsevich (Ukraine), V. Koshlyakov(Ukraine), I. Lukovskii (Ukraine), G. Liu(China), V. Matrosov (Rusiia), K. Peiffer(Belgium), F. Pfeiffer (Germany), W.Respondek (France), V. Rumyantsev (Russia),A. Savchenko (Ukraine), W. Schiehlen(Germany), V. Shevchenko (Ukraine), V.Storozhev (Ukraine), H. Troger (Austria), S.Vasilyev (Russia), V. Vujichich (Yugoslavia)Organising committee: A. Kovalev (Chair,Institute of Applied Mathematics and Mechanicsof the National Academy of Sciences ofUkraine), A. Stupin (Co-chair, Donetsk NationalUniversity), B. Konosevich (secretary, IAMMNASU)Proceedings: on presentation of the programmecommittee, selected proceedings to be publishedin scientific journalsLocation: the boarding-house of DonetskNational University on the Azov sea coastDeadlines: for pre-registration, 31 January; forabstracts, 31 MayInformation:e-mail: konos@iamm.ac.donetsk.uaWeb site:http://www.iamm.ac.donetsk.ua/conf2002.html4-7: International Conference on DynamicalMethods for Differential Equations,Valladolid, SpainInformation:Web site: http://wmatem.eis.uva.es/~dmde02/[For details, see EMS Newsletter 41]8-13: ALGORITMY 2002, Conference on

Scientific Computing, High Tatra Mountains,Podbanske, SlovakiaTheme: applied mathematics, numericalmethods, computational science andvisualisationScope: computational realisations and analysisof algorithms solving real problems from allbranches of sciences, engineering, technology,medicine, finance and other applicationsTopics: computational fluid dynamics, non-linear heat and mass transfer, modelling of flowin porous media, image processing andcomputer vision, data analysis and patternrecognition, computational finance, freeboundary problems, inverse problems, scientificvisualisation, software for scientificcomputationsMain speakers: A. Bourlioux (Montreal), F.Cao (Paris), R. Eymard (Paris), M. Falcone(Rome), P. Frolkovic (Heidelberg/Bratislava), J.Fuhrmann (Berlin), M. Gander (Montreal) R.van Keer (Ghent), M. Lukacova-Medvidova(Brno), M. Ohlberger (Freiburg), M. Rumpf(Duisburg), A. Schmidt (Bremen), J.A. Sethian(Berkeley), G. Wittum (Heidelberg)Programme: invited plenary lectures, 25-minutes contributed talks, poster sessionCall for papers: refereed conferenceproceedings of contributed lectures will bepublished before the conference. Papers relatedto the topics of the conference are invited(previous issues are at http://www.iam.fmph.uniba.sk/amuc/_vol70n1.html).Proceedings of plenary lectures and selectedpapers of participants will appear after theconference in the Springer-Verlag journalComputing and Visualization in ScienceProgramme committee: E. Baensch (Berlin), P.Brunovsky (Bratislava), G. Dziuk (Freiburg), W.

Jaeger (Heidelberg), J. Kacur (Bratislava), J.Komornik (Bratislava), G. Meyer (Atlanta), K.Mikula (Bratislava), M. Rumpf (Duisburg), J.A.Sethian (Berkeley), M. Vajtersic (Bratislava), G.Wittum (Heidelberg) Organising committee: A. Handlovicova, M.Komornikova, Z. Kriva, K. Mikula, P. Struk, D.Sevcovic, M. StevulovaLocation: Hotel Permon, PodbanskeDeadlines: preliminary registration, 31December; submission to proceedings, 30 April;registration, 31 May; payment, 31 May (regularconference fee); final submission of revisedversion to proceedings, 21 June; lateregistration, 15 August; final payment, 15August (late conference fee)Information:Web site: http://www.math.sk/alg2002e-mail: algoritm@vox.svf.stuba.sk10-20: Advanced Course on Geometric 3-Manifolds, Bellaterra, Barcelona, SpainCoordinator: Joan PortiInformation:Web site: http://www.crm.es/geom-mani20-25: International Conference onComputational Methods in Science andEngineering (CMMSE-2002), Alicante, SpainTheme: numerical analysis, computationalphysics, computational chemistry Topics: celestial mechanics, computationalchemistry and physics, computationalengineering, computational mathematics,computational statistics, high-performancecomputing, industrial mathematics,mathematical economics and finance,mathematical models for the information societyChairs: J.M. Ferrandiz (Spain), D.L.Richardson (USA) (celestial mechanics), E.Brandas (Sweden), D. Truhlar (USA), D. Belkic(Sweden) (computational chemistry andphysics), K.J. Bathe (USA), R. Lewis (UK)(computational engineering), J. Butcher (NewZealand), D.J. Higham (UK), T. Simos(Greece), J. Xu (USA) (computationalmathematics), M.J. Bayarri (Spain)(computational statistics), H. Arabnia (USA),C.J.K. Tan (Canada) (high performancecomputing), C. Dawson (USA) (industrialmathematics), M. Ojeda (Spain), P. Vojtás(Eslovaquia) (mathematical models for theinformation society)Proceedings: selected papers will appear inseveral special issues of the Journal ofComputational and Applied Mathematics(www.elsevier.nl/inca/publications/), and theJournal of Computational Methods in theSciences and Engineering(www.demon.co.uk/cambsci/jcmse.html)Location: University of Alicante, SpainDeadline: for abstracts, 15 DecemberInformation:e-mail: cmmse2002@ua.esWeb site: www.ua.es/cmmse2002/23-27: Ramification in Arithmetic andGeometry, Paris, FranceOrganisers: A. Abbes (Paris), B. Erez(Bordeaux), T. Saito (Tokyo)Location: Institut Galilee, Universite Paris 13Information:http://www-math.math.univ-paris13.fr/~ramifica/

9-11: 7th Conference on Shell Structures,

October 2002

Theory and Applications (SSTA2002),Gdañsk-Jurata, PolandAim: to bring together scientists, designers,engineers and other specialists in shellstructures in order to discuss importantresults and new ideas in this field of activityTopics: theory and analysis of shells (linearand non-linear theory, constitutive laws,shells and plates with internalmicrostructure, hybrid and branchedstructures, beam-shell interaction, stability,dynamics, optimisation, reliability,sensitivity, limit load analysis); numericalanalysis of shell structures and elements(computer methods, analysis of non-standardproblems, development of softwarepackages); design and maintenance of shellstructures (industrial applications in civil,power, mining and mechanical engineering,and in the automotive, shipbuilding,aerospace and chemical processingindustries, shell design codes and procedures(e.g. Eurocode), case studies of various shellstructures and failure problems)Programme: general lectures and contributedpapers presented as lecturesLanguages: English and PolishScientific committee: Wojciech Pietraszkiewicz(chairman), Jan Awrejcewicz, JacekChrócielewski, Micha³ Kleiber, Pawe³K³osowski, Piotr Konderla, Marian Królak,Tomasz Lewiñski, Czes³aw Szymczak,Krzysztof Winiewski, Rocis³aw Tribi³³o,Zenon Waszczyszyn, Czes³aw Woniak, JerzyZió³koOrganising committee: Department ofStructural Mechanics, Faculty of CivilEngineering, Technical University of Gdañsk,PolandProceedings: accepted abstracts (2 pages) willbe included in the conference book of abstracts,available for the participants at registration.Full-length manuscripts of selected papers willbe further considered for publication in a specialvolume of a recognised technical journalLocation: Hotel Neptun in the leisure region ofthe Hel Peninsula on the Baltic Sea(http:\\www.hotelneptun.gda.pl)Grants: a limited number of fellowships fordistinctive young researchers (less than 35 yearsold) from Eastern Europe, to cover participationin the Conference but not travelFees: registration fee, which covers full-boardaccommodation and the book of abstracts, isapproximately $300 US; $250 US foraccompanying personsDeadlines: for pre-registration, 31 December;for submission of 2-page abstracts, 30 AprilInformation: contact SSTA2002 OrganisingCommittee, Department of StructuralMechanics, Faculty of Civil Engineering,Technical University of Gdañsk, G.Narutowicza11/12, 80-952, Gdañsk, Poland; tel: +48-58-347-21-47; fax: +48-58-347-16-70e-mail: ssta2002@pg.gda.plWeb site: http://www.pg.gda.pl/ssta2002

5-7: 4th IMACS Symposium onMathematical Modelling, Vienna, AustriaInformation:Web site:http://simtech.tuwien.ac.at/MATHMOD[For details, see EMS Newsletter 41]

February 2003

CONFERENCES

EMS December 2001 33

Books submitted for review should be sent to thefollowing address:Ivan Netuka, MÚUK, Sokolovská 83, 186 75Praha 8, Czech Republic.

S. Abbott, Understanding Analysis,Undergraduate Texts in Mathematics,Springer, Berlin, 2001, 257 pp., DM 79,ISBN 0-387-95060-5This book aims to build up the elements ofanalysis properly that is, with a goodlevel of understanding. It contains funda-mental results on real numbers, limits andcontinuity, differentiation, sequences,sums of functions and the Riemann inte-gral. In many places, the book could beused for an introductory analysis course.In others, the material presented in thetext would be appropriate after a calculuscourse. The authors intention was torestore intellectual liveliness of the courseby offering to beginning students access tosome truly significant achievements of thesubject. In other words, he tries to presentrelatively advanced topics in an accessibleway, and thus make the course interestingand worthy of effort.

Among the topics treated in the book arecompleteness of the reals, double summa-tion and products of series, Baires theo-rem, continuity of derivatives, a continuousnowhere-differentiable function (Takagiapproach) and Lebesgues criterion forRiemann integrability. In the last chapter,the author shows that for the generalisedRiemann integral all derivatives are inte-grable, and that the set of continuous func-tions on a compact interval I, differen-tiable at least at a point, is of the first cate-gory in C(I), and presents basic results onFourier series.

This book will be useful for gifted stu-dents for supplementary reading to a basicanalysis course or for students not special-ising in mathematics who wish to put thismaterial on a solid basis. (jive)

E. M. Alfsen and F. W. Shultz, StateSpaces of Operator Algebras. Basic Theory,Orientations and C*-products, Mathematics:Theory and Applications, Birkhäuser, Boston,2001, 350 pp., DM 170, ISBN 0-8176-3890-3 and 3-7643-3890-3This monograph is devoted to the theoryof state spaces of C*-algebras and vonNeumann algebras and their geometry.The states determine representations ofthe algebra, and its algebraic stucture isencoded in the geometry of the state space.The theory of operator algebras has wideapplications to physics, and there haverecently been applications to various fieldsof pure mathematics (foliations and knottheory, Banach manifolds and infinite-dimensional holomorphy).

The introduction includes convexity,ordered vector spaces and ordered alge-

bras, elementary dimension theory in lat-tices, algebras with involution and orderderivation. A self-contained elementaryintroduction to C*-algebras and vonNeumann algebras is presented in Chapter2. The next chapter presents the duality ofthe ideal structure of C*-algebras and vonNeumann algebras and the facial structureof the state space; this chapter alsoincludes an order-theoretic charac-terisation of compressions. Chapter 4 isdevoted to the normal state space of thealgebra of all bounded operators on aHilbert space, explaining also how it canbe inscribed in a Euclidean ball and how itslattice of faces corresponds to theGrassmannian. Chapter 5 concerns states,representations and orientations of C*-algebras. The next chapter surveys theelements of structure theory and continueswith a study of symmetries and reflectionsin von Neumann algebras. Orientationsand von Neumann algebras form the finalchapter.

This volume contains complete proofs ofbasic results and commentaries onadvanced topics of independent interestwith references to the literature, and a dis-cussion of applications to physics. Themonograph is designed for experts inoperator algebras, as well as for graduatestudents and researchers interested in thefield. It can also serve as a quick intro-duction to C*-algebras and von Neumannalgebras for any mathematician who wantsto learn the subject. The book is under-standable with a basic knowledge of realand complex analysis, measure theory andfunctional analysis, and spectral theory.(jl)

J. W. Anderson, Hyperbolic Geometry,Springer Undergraduate Mathematics Series,Springer, London, 1999, 230 pp., DM 59,ISBN 1-85233-156-9 This textbook is an introduction to non-Euclidean geometry designed for under-graduate students. It is based mainly onthe Poincaré half-plane model, and is writ-ten in a very understandable way; with onlyelementary knowledge needed for its read-ing.

In Chapter 1, the author defines thePoincaré model and its points and lines.In the next chapter, the group of transfor-mations preserving the system of lines iscarefully studied. Chapter 3 introducesthe metric properties of geometry asinvariants of this group, and Chapter 4briefly exposes the possibility of gettingnew models by transferring the half-planegeometry by diffeomorphisms. In Chapter5, convexity, area and trigonometry arestudied and the Gauss-Bonnet Formula isproved. Chapter 6 presents the discretesubgroups of the group of motions.

The book is well structured. Each indi-

vidual chapter concludes with exercisesthat are substantial for understanding whatfollows. The typography of the book is notideal and the notation is a bit complicated.The topic of the book is very geometrical,and more pictures could have been expect-ed. In particular, many of the computa-tions could be nicely complemented by pic-tures appealing to geometrical intuition.Despite these remarks, the textbook is agood and useful introduction to hyperbol-ic geometry, and can be recommended forundergraduate courses. (zs)

D. H. Armitage and S. J. Gardiner,Classical Potential Theory, SpringerMonographs in Mathematics, 2001, 333 pp.,DM 159, ISBN 1-85233-618-8 Over the past century, the potential theoryof Laplaces equation (classical potentialtheory) has undergone its most outstand-ing and rapid development. Everybodyworking in new branches of potential theo-ry (non-linear theories, probabilistic andaxiomatic approaches to potential theory,pluripotential theory, functions of one ormore complex variables, etc.) should bene-fit from the knowledge of classical theory.There are brilliant textbooks and mono-graphs on potential theory, such as thoseof Brelot, Helms, Doob, Landkof. Thebook by Armitage and Gardiner follows themost classical text of Helms and comple-ments it with new results and approaches.

The first chapter introduces and sum-marises the main properties of harmonicfunctions (Laplaces equation, mean valueproperties, convergence properties, theKelvin transform, the Poisson integral andHarnacks inequalities). There follows achapter on harmonic polynomials.Elementary properties and new resultsconcerning subharmonic functions aredescribed in Chapter 3 (approximation ofsubharmonic functions by smooth ones,convexity and subharmonicity and har-monic majorants). The next chapters aredevoted to a penetrating study of poten-tials (Green functions, the Riesz decompo-sition, the distributional Laplacian, classi-cal boundary limit theorems), polar setsand capacity (removable singularities,reduced functions, Choquet capacitabilitytheorem, logarithmic capacity, Hausdorffmeasure and capacity) and the classicalDirichlet problem (Perron-Wiener-Brelotsolutions, harmonic measure, negligiblesets, superharmonic extension). The finalthree chapters are deeper and introducetopological concepts from potential theo-ry: the fine topology (thin sets, fine limits,Wieners criterion, harmonic approxima-tion), the Martin boundary (minimal har-monic functions, the Martin representa-tion, the boundary Harnack principle andthe Martin boundary of Lipschitz domains)and boundary limits (swept measures andthe Dirichlet problem for the Martin com-pactification, minimal thinness, the Fatou-Naïm-Doob theorem).

Each chapter concludes with a set ofexercises, either routine or leading toresults from the research literature. At theend of the book, there are brief historicalnotes and an Appendix where less elemen-

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Recent booksRecent booksedited by Ivan Netuka and Vladimír Sou³ek

tary results from analysis are stated withoutproof. The monograph is designed toserve both as a general textbook and as adetailed exposition of the classical topics inpotential theory. It should be accessible tograduate students and researchers inter-ested in the field of potential theory, andwill be understandable with a basic knowl-edge of first-year graduate courses inanalysis. A knowledge of calculus in high-er dimensions, measure theory, very basictopology and linear algebra are required.(jl)

B. Bakalov and A. Kirilov, Jr., Lectures onTensor Categories and Modular Functors,University Lecture Series 21, AmericanMathematical Society, Providence, 2001, 221pp., US$29, ISBN 0-8218-2686-7The book narrates a big adventure of the1990s, a grand unification of three seem-ingly unrelated structures: modular tensorcategories, 3-dimensional topologicalquantum field theories (3D-TQFTs) and 2-dimensional modular functors. Tensorcategories are categories with a multiplica-tion that generalises the tensor product inthe category of vector spaces. Modulartensor category is then a tensor categorywith a finite number of simple objects sat-isfying certain non-degeneracy conditions.The main examples come from represen-tations of quantum groups at unity.

A 3D-TQFT is a rule that assigns to each2-dimensional manifold a vector space (thestate space) and to each 3-dimensionalmanifold with boundary (thought of as abordism of 2-manifolds) a linear operator.A slight generalisation allows for 2-mani-folds with marked points and 3-manifoldswith framed tangles. A 2-dimensionalmodular functor is a functor from themodular category of 2-dimensional mani-folds and isotopy classes of their homeo-morphisms to the category of vectorspaces. An equivalent definition can begiven in terms of flat connections on themoduli space of curves.

The authors explain that these notionsare essentially equivalent. The equivalenceof tensor categories and 3D-TQFTs ismediated by Resetikhin-Turaev invariantsof links and 3-manifolds, while the equiva-lence with modular functors is based onresults of Moore and Seiberg and uses thepair of pants decomposition of surfaces.The book assumes some preliminaryknowledge of algebraic/differential geome-try and category theory, and is addressedat graduate students and researchers inter-ested in this beautiful part of mathematicswith a strong physical flavour. (mm)

R. G. Bartle, A Modern Theory ofIntegration, Graduate Studies in Mathematics32, American Mathematical Society,Providence, 2001, 458 pp., US$59, ISBN 0-8218-0845-1The Kurzweil-Henstock theory of integra-tion is well described in this book. ForKurzweil-Henstock integration, first-yearstudents have no essential difficulties inunderstanding the main idea of definingthe integral, because of its similarity withthe Riemann integral. The difference

between the definitions of Kurzweil-Henstock and Riemann is at first almostimperceptible. On the other hand,Riemanns approach gives an integral thatis very weak from a practical point of view;this was why Lebesgues theory of integra-tion was created at the beginning of thelast century. The Kurzweil-Henstock theo-ry is more general than the Lebesgue oneand it overcomes the problem that theLebesgue integral does not integrate deriv-atives in general. Another advantage ofKurzweil-Henstock integration is that toexplain it, only the concept of the realnumbers is needed (the theorem on thesupremum) and everything can be done onthis basis, including very general conver-gence results. Along these lines, theauthor explains the theory for real func-tions defined on compact one-dimensionalintervals in the first part of the book, andthen extends it for infinite intervals in thereals. Links with measure theory, measur-ability and the Lebesgue integral are pre-sented, even though they are not neededfor presenting the Kurzweil-Henstock the-ory (this is one of the merits of the theory).The topics are excellently motivated andthe book contains many well-chosen exer-cises, some of them solved in the conclud-ing part of the book. (s)

D. C. Benson, The Moment of Proof.Mathematical Epiphanies, Oxford UniversityPress, 2001, 331 pp., £9.99, ISBN 0-19-513919-4 The author acquaints the reader with manytopics of mathematics and with relatedinteresting curiosities. But the main aim ofthis book is to share with a wide range ofreaders the pleasure of mathematicalthinking and the joy of discovery. Readerswill frequently experience the pleasure of asudden insight into a mathematical prob-lem, and many will understand what itmeans when somebody speaks about thebeauty of mathematics, about the eleganceof mathematical proofs, and about thecharm of mathematical ideas. (ec)

T. Beth, D. Jungnickel and H. Lenz,Design Theory, Vols. 1, 2, Encyclopedia ofMathematics and its Applications 69 and 78,Cambridge Univesity Press, 1999, 607 and492 pp., £60 and £60, ISBN 0-521-44432-2and 0-521-77231-1This is a new edition of a respectable two-volume set devoted to the study of designs(set systems satisfying strong regularityassumptions). If the first 1985 edition wasthe first comprehensive treatment of thesubject, the second edition comes at a timewhen there are numerous books that treatthe subject in various aspects and depth.The text has been thoroughly revised andcomplemented to meet new demands andcapture some of the latest developments.The authors succeed in doing so, and thepresent volumes present one of the mostthorough treatments of the subject. It ishighly recommended for study as well asfor content.

The first volume includes examples andbasic definitions, combinatorial analysis ofdesigns, and chapters on groups and

designs, Witt designs, Mathieu groups andhighly transitive designs, a discussion ofdifference sets and regular symmetricdesigns, and difference families. The sec-ond volume has chapters on recursive con-structions, transversal designs and nets,asymptotic existence theory, characteristicof classical designs, and their applications.Together with an appendix, tables, bibli-ography, a list of symbols and an index,there are 1093 pages in total. (jnes)

S. Billey and V. Lakshmibai, SingularLoci of Schubert Varieties, Progress inMathematics 182, Birkhäuser, Boston, 2000,251 pp., DM 118, ISBN 0-8176-4092-4 and3-7643-4092-4 The study of Schubert varieties started inthe nineteenth century as a part of classicalprojective geometry. A modern treatmentof the subject became possible through theworks of Ehresmann, Chevalley, Bernstein,Gelfands, Demazure, and the authors ofthis book. Schubert varieties now provideone of the best understood examples ofcomplex projective varieties, and theirproperties have been studied in manypapers. Thus, the publication of the bookis a very timely event. Already by 1964Chevalley had shown that Schubert vari-eties are non-singular in codimension 1,and in 1973 Demazure discovered non-smooth Schubert varieties. In the past fif-teen years, many major developments inthe field have taken place, making it possi-ble to do more elaborate computations onsingular loci and to solve questions con-cerning the smoothness of Schubert vari-eties. In these questions, contemporarytechniques from algebraic geometry, rep-resentation theory and combinatorics areneeded. All of these techniques areexplained with maximum benefit toresearchers in the field or graduate stu-dents. (ae)

J. Billingham and A. C. King, WaveMotion, Cambridge Texts in AppliedMathematics, Cambridge University Press,2000, 468 pp., £24.95, ISBN 0-521-63257-9 and 0-521-63450-4 Waves are everywhere. This is the conclu-sion that will make after reading the book.The authors remind us that whenever wesee or hear anything, we do so because ofthe existence of waves. Every heartbeatand every nerve impulse owes its existenceto electrochemical waves. The authorspresent the topic of waves for advancedundergraduates in applied mathematics.

The book is divided into three sections.The first section begins with a very basicintroduction: no special knowledge isneeded in order to understand the book.This section deals with the linear theory ofwaves and covers a wide range of impor-tant applications, such as acoustics, gravitywaves, shallow water waves, waves in elasticbodies and electromagnetism. The secondpart of the book presents the basics of thenon-linear theory of waves. The theory isagain explained through a wide range ofapplications, including shock waves in traf-fic, gas dynamics, non-linear water waves,molecular diffusion, and the transmission

RECENT BOOKS

EMS December 2001 35

of nerve impulses. The last part of thebook covers more advanced topics, such asBurgers equation, the Kortweg-de Vriesequation and the non-linear Schrödingerequation.

The book is written very clearly, withmany diagrams and figures accompanyingthe text. There are also photographs,which are rarely to be found in mathemat-ical textbooks. At the end of each chapterthere are sufficient numbers of exercises,so that readers can test their understand-ing of the topics. Although the solutions toexercises are not included in the book, theauthors provide an e-mail address fromwhich fully worked solutions can beobtained. The book contains three shortappendices that present different systemsof coordinates, some results of vector cal-culus, and a table of useful physical con-stants. This textbook will be valuable forstudents of mathematics who wish to applytheir mathematics to physics and otherfields. (tf)

A. Björner, M. Las Vergnas, B. Sturmfels,N. White and G. Ziegler, OrientedMatroids, Encyclopedia of Mathematics and itsApplications 46, Cambridge University Press,1999, 548 pp., £30, ISBN 0-521-77750-XThis is the second paperback edition ofthis book. The main topic of the book, ori-ented matroids, is an abstract axiomaticgeneralisation of hyperplane arrange-ments, point configurations and convexpolytopes in geometry, directed graphs indiscrete mathematics, and in many othersituations. The book describes the basicsof the subject and its applications to otherareas of mathematics.

In this revised edition there is a newappendix with a summary of research donesince the publication of the first edition in1993. The authors have also updated andsubstantially expanded the bibliography,which now has more than 50 pages. Thebook describes a subject situated at thecrossroads of many fields of mathematics,and will therefore be interesting for math-ematicians in geometry, representationtheory, topology, algebraic geometry andcomputer science, as well as for chemists.(vs)

D. M. Bressoud, Proofs andConfirmations, Spectrum Series, CambridgeUniversity Press, 1999, 274 pp., £17.95,ISBN 0-521-66170-6 and 0-521-66646-5The area of the book is algebraic combina-torics. The main problem discussed hereis a particular question: to find a formulafor the number of alternating sign matricesof order n (the non-trivial entries of analternating sign matrix can be only +1and 1, the sum of the entries in each rowor column is 1, and the non-zero entries ineach row or column alternate in sign). Theauthor presents a description of the evolu-tion of the subject, starting in the 1980sand ending more than ten years later,leading to a proof of the conjectured for-mula.

This is a fascinating story, going fromclassical invariant theory to partitions,symmetric functions, tableaux, various

forms of hypergeometric series and vertexmodels in statistical mechanics, via four-teen interrelated conjectures, to the finalgoal. The book is written in a very interest-ing and attractive way, full of ideas, pic-tures, photographs, historical remarks andmany exercises. Furthermore, the specialproblem described above provides an occa-sion for the author to discuss very interest-ing and basic questions concerning mathe-matics as a whole what are the roles ofconjecture and proof in mathematics?, ormore generally, how do mathematiciansreally do research? This is an excellentbook which can be recommended withouthesitation, not only to specialists in thefield, but to any mathematician with timeto read something interesting and nicelywritten. (vs)

P. Le Calvez, Dynamical Properties ofDiffeomorphisms of the Annulus and of theTorus, SMF/AMS Texts and Monographs 4,American Mathematical Society, SociétéMathématique de France, Providence, 2000,105 pp., US$21, ISBN 0-8218-1943-7 Monotone twist maps are a useful tool inthe theory of conservative and dissipativedynamical systems. The first two chapterspresent a survey of approaches to the the-ory of such maps, with generalisations, andseveral motivating examples are given.The Aubry-Mather variational approach isexplained, and criteria for the existence ofperiodic orbits are discussed. The topo-logical approach is used for a descriptionof the dynamics on invariant curves. Thesecond chapter asserts that each diffeo-morphism of the closed annulus isotopic tothe identity can be represented as a com-position of monotone twist maps, and themethods in the first part are used to studydiffeomorphisms isotopic to the identity.New proofs of some results concerning therotation set and periodic orbits of diffeo-morphisms of the circle are presented. (s)

B. Chazelle, The Discrepancy Method,Randomness and Complexity, CambridgeUniversity Press, 2000, 463 pp., £40, ISBN 0-521-77093-9This book is written by one of the leadersin the field. It presents a rapidly develop-ing field in admirable breath and depth,and is written in a beutiful style. From thedust jacket description: This book tells thestory of the discrepancy method in a fewshort, independent vignettes. It is aneclectic tale that features, among othertopics, communication complexity,pseudorandomness, rapidly mixingMarkov chains, points on the sphere viamodular forms, derandomization, convexhulls, Voronoi diagrams, linear program-ming, geometric sampling, VC-dimensiontheory, minimum spanning trees, linearcircuit complexity, and multidimensionsearching. The topics discussed includecombinatorial discrepancy, upper andlower bound techniques, sampling, geo-metric searching, complexity lowerbounds, convex hulls and Voronoi dia-grams, linear programming and exten-sions, pseudorandomness, communicationcomplexity, minimum spanning trees (this

contains the best description of the fastestknown deterministic algorithm (due to theauthor: 53 pages).

There are three appendices summaris-ing the necessary background material(probability theory, harmonic analysis andconvex geometry). Taken with Matoueksbook (Geometric Discrepancy: An IllustratedGuide, Springer, 1999), discrepancy theoryis fortunate to have two complementarybooks of excellent quality written by lead-ers of the field. This is the first bookdevoted to the discrepancy method. (jnes)

F. Chung and R. Graham, Erdös onGraphs, A. K. Peters, Ltd., Wellesley, 1999,142 pp., US$25, ISBN 1-56881-079-2 This is a collection of Paul Erdõs (mostlyopen) problems related to graphs andhypergraphs, with commentary. The top-ics treated in the book include extremalRamsey theory, colouring, packing andcovering, random graphs and enumera-tion, hypergraphs, and infinite graphs.This is complemented by personal remi-niscences by the authors, and by A.Vászonyi, one of Erdõss oldest collabora-tors. This book also contains an impressivelist of survey articles devoted to P. Erdõs,many of which are collected in: Mathematicsof Paul Erdõs I, II (ed. R. L. Graham and J.Neetøil), Springer-Verlag, 1996. It wouldbe useful to have similar collections inother branches of Erdõss activity num-ber theory, in particular. (jnes)

C. W. Curtis, Pioneers of RepresentationTheory: Frobenius, Burnside, Schur andBrauer, History of Mathematics 15, AmericanMathematical Society, Providence, 1999, 287pp., US$49, ISBN 0-8218-9002-6Representation theory has made enor-mous progress in the last century. Thisbook returns to its roots, to the representa-tion theory of finite groups. The principalfigures in its development were four excel-lent mathematicians Frobenius,Burnside, Schur and Brauer. Building onideas concerning characters of finiteabelian groups, the first steps in the struc-ture theory of finite groups, and researchin finite-dimensional associative algebra,they created (with others) a beautiful theo-ry that was subsequently a model andinspiration for further evolution of therepresentation theory of Lie groups. Thebook concentrates on the mathematicalaspects of their original papers anddescribes their content and methods, usingmodern language. The historical aspectsare treated as well: a full account of the his-tory of the subject can be found in papersby Thomas Hawkins. This very nice book isaccessible with a basic knowledge of alge-bra, and is recommended. (vs)

H. G. Dales, Banach Algebras andAutomatic Continuity, London MathematicalSociety Monographs New Series 24, ClarendonPress, Oxford, 2001, 907 pp., £110, ISBN 0-19-850013-0 This bulky monograph presents a detailedmodern account of basic Banach algebratheory. The main chapters are devoted toconnections between algebraic and topo-

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EMS December 200136

logical structures for general Banach alge-bras, as well as for particular examples.The author studies when (and how) alge-braic structures determine various aspectsof topological ones.

In the first chapter, the algebraic back-ground is established (including orderedsets, algebraic semigroups, ideals, mod-ules, radicals, spectra, valuation algebras,cohomology and involutions); specialattention is paid to the use of logic and settheory. The next chapter explains the gen-eral theory of Banach algebras as well assome of the theory of more general topo-logical algebras. This chapter also con-tains sections on the Gelfand theory, func-tional calculus, Banach algebras of opera-tors and Banach modules. The third chap-ter is devoted to Banach algebras with aninvolution (including C*-algebras andgroup algebras). Chapter 4 presents thetheory of commutative Banach algebras.After a general introduction, the authorstudies particular examples (such as alge-bras of continuous functions, uniform alge-bras, algebras of differentiable andLipschitz functions, abelian group alge-bras, Banach algebras of power series andconvolution algebras). The last chapter,the culmination of the book, deals withautomatic continuity theory itself. In par-ticular, it treats uniqueness of norm, sepa-rating spaces and the stability lemma, con-tinuity ideals and singularity sets, the mainboundedness theorem, linear functionals,continuous and discontinuous derivations,and embedding algebras in Banach alge-bras.

At the end of the book, an appendixgives some background from topologicaland metric spaces, complex and functionalanalysis, measure theory, integration andanalytic spaces, together with an index ofsymbols, theorems, identities and exam-ples. A general index and an extensive listof references are included. This volumi-nous text is recommended to graduate stu-dents and experts in the field of Banachalgebras, and to those working in function-al analysis and in algebra. (jl)

O. Debarre, Tores et variétés abéliennescomplexes, Cours Spécialisés 6, SociétéMathématique de France, Paris, 1999, 125pp., ISBN 2-86883-427-2 The main topic treated in this book is theclassical theory of abelian tori. At thebeginning of the book, the author brieflyreviews the classical facts on lattices andelliptic curves (complex tori, Weierstrassfunction, divisors, theta functions, theRiemann-Roch theorem and modulispaces of elliptic curves). Taking these asmotivation, the author presents a discus-sion of many questions concerning com-plex abelian varieties in higher dimen-sions. An abelian variety is a complextorus that admits a holomorphic embed-ding in a projective space: characterisingabelian varieties is the central problem inthis book. To answer it, the author usesmodern tools holomorphic line bundles,cohomologies with values in a sheaf andChern classes. This part of the book isquite elementary, and requires only a very

modest knowledge; all necessary tools areintroduced in the text. The last two chap-ters are more advanced. Chapter 7 con-tains a discussion of moduli spaces ofpolarised abelian varieties. The final chap-ter contains recent results on the geometryand topology of subvarieties of a complextorus, and needs much more background.Most of the results in this book are fullyproved and the presentation of ideas isunderstandable. This small booklet is verysuitable for a course on this topic. (vs)

E. G. Effros and Z.-J. Ruan, OperatorSpaces, London Mathematical SocietyMonographs New Series 23, Clarendon Press,Oxford, 2000, 363 pp., £60, ISBN 0-19-853482-5Any normed linear space can be regardedas a concrete function space that is, as alinear space of bounded functions on a setequipped with the uniform norm.Analogously, a (concrete) operator space isa linear space of bounded operators on aHilbert space. The authors define an(abstract) operator space by axiomatisingthe properties of concrete operator spaces.Roughly speaking, operator spaces are lin-ear spaces equipped with an operatorspace matrix norm. The roots of such atheory of operator spaces go back to thefamous Heisenberg uncertainty principle,together with the mathematical work ofJordan, von Neumann and Weyl, and lead-ing to research in the field of algebras ofbounded operators on Hilbert spaces.This monograph is concerned with a morerecent innovation, the quantisation ofBanach space theory.

In a preliminary chapter the reader isintroduced to spaces with matrix coeffi-cients. It is followed by a chapter on thethree fundamental results in operator the-ory, and complete proofs of Ruans repre-sentation theorem, the Arveson-Wittstocktheorem (a generalisation of the Hahn-Banach theorem) and the Paulsen-Wittstock decomposition theorem for com-plete contractions; there is also a short sec-tion on a characterisation of injective oper-ators spaces. The next chapter concernstensor products (projective and injectivetensor products, the Haagerup tensorproduct). These are used to generaliseGrothendiecks theory of approximationproperties. This part discusses nuclear,integral and absolutely summing map-pings, including the Dvoretsky-Rogers the-orem for operator spaces. In Chapter 4,the central part of the text, the main topicsof nuclearity, exatness and local reflexivityare presented. The final chapter is devot-ed to the algebraic applications of operatorspace theory (non-commutative harmonicanalysis, including quantised Banach alge-bras and Fourier algebras on locally com-pact groups). An appendix summariseselementary results from functional analysis(Banach and Hilbert spaces, C*-algebras,von Neumann algebras, together with abrief list of operator algebras). Theauthors claim that their goal in this mono-graph has been to explain the deep analo-gy between linear spaces of bounded func-tions and linear spaces of bounded opera-

tors and that operator space theory willprovide Banach space theorists with excit-ing new vistas for research.

The monograph is designed for gradu-ate students and researchers interested inthe field, and can be understood with arudimentary knowledge of functionalanalysis, and in particular of Banach spacetheory. (jl)

B. Engquist and W. Schmid (eds.),Mathematics Unlimited 2001 andBeyondd, Springer, Berlin, 2001, 1236 pp.,179 fig., DM 79, ISBN 3-540-66913-2 The aim of the editors is to give responsesand insights to the question: What is thefuture of mathematics in the new millenni-um? through this unique collection ofmore than sixty contributions by leadingexperts in various fields of mathematics,and to provide the reader with a view ofgreat variety and the vitality of mathemat-ics as we enter the new millennium.Although a similar goal was followed inanother recent collection, Mathematics:Frontiers and Perspectives, edited by V.Arnold, M. Atiyah, P. Lax and B. Mazur,significant attention is here paid to thenewest interactions between mathematicsand other disciplines, such as bioscience,economics, material science, communica-tions and computer science, and it is alsomore focused on applied mathematics.Because of its wide scope, the reader cancertainly find within its pages many excit-ing and thought-provoking papers. (jmal)

R. Estrada and R. P. Kanwal, SingularIntegral Equations, Birkhäuser, Boston,2000, 427 pp., DM 138, ISBN 0-8176-4085-1 and 3-7643-4085-1This is a textbook on singular and convo-lution integral equations. After presentingthe basic mathematical tools, the authorsoutline the basic theory of convolutionequations. In Chapter 3, direct methods ofsolutions of convolution equations areexplained, and in Chapter 4, singular inte-gral equations with variable Hölder contin-uous coefficients are discussed, when therange of integration is either a closed con-tour or an open arc (the so-calledCarleman equation). Chapters 5 and 6deal with distributional solutions of singu-lar integral equations on a compact inter-val, as well as on the entire real line; theHilbert transform is used here. Integralequations with logarithmic kernels with apolynomial are solved in ordinary andgeneralised spaces of functions in Chapter7. In Chapter 8, the classical Wiener-Hopfequation with absolutely integrable kernelis solved. Finally, Chapter 9 investigatesdual integral equations. The book con-tains instructive examples and exercisesfor each particular class of integral equa-tions. It should be very useful for engi-neers and students. (s)

M. Flexor, P. Sentenac and J.-C. Yoccoz(eds.), Géometrie complexe et systèmesdynamiques, Astérisque 261, SociétéMathématique de France, Paris, 2000, 443pp., FRF 450, ISBN 2-85629-081-7 This volume consists of a representative

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collection of fifteen papers on dynamicalsystems, presented at a meeting held in1995 on the occassion of Adrien Douadyssixtieth birthday. Most of the papers con-cern various aspects of iterations of realpolynomials, especially quadratic ones(Julia and Mandelbrot sets, invariant andSinai-Ruelle-Bowen measures, Douady-Hubbard theory, and denseness of systemswith finitely many attractors of specialproperties). Also studied are hyperbolicrational maps, Lampert maps, the one-parameter generalisation of the Lorenzmodel and holomorphic foliations in thecomplex plane. These proceedings areaccessible to experts in dynamical systems,and the lengthy introductions of mostpapers may also make them available to awider mathematical community. (jmil)

L. E. Fraenkl, Introduction to MaximumPrinciples and Symmetry in EllipticProblems, Cambridge Tracts in Mathematics128, Cambridge University Press, Cambridge,2000, 340 pp., £45, ISBN 0-521-46195-2 This book presents the basic theory of thesymmetry of solutions to second-orderelliptic partial differential equations, bymeans of the maximum principle. InChapter 0, the author sets up the basicnotation and termonology. The introduc-tory Chapter 1 is then intended to moti-vate further investigation. Chapter 2 dealswith maximum principles for sub-solutionsof elliptic partial differential equations ofthe second order. In Chapter 3 the authorstudies the behaviour of positive solutionsof the equation ∆u + f(u) = 0, in a bound-ed symmetric set Ω with u = 0 on theboundary of Ω. As a consequence of theseresults, he shows the spherical symmetry ofthis solution in the case of a ball. InChapter 4 the spherical symmetry of a pos-itive solution of the equation ∆u + f(u) =0 in Rm is shown. Chapter 5 concerns themonotonicity of positive solutions of theequation ∆u + b.grad u + f(u) = 0 in abounded set. Each paragraph ends withexercices.

The text is accompanied by five appen-dices. Appendix A is devoted to the studyof the Newtonian potential as a solution ofthe Poisson equation, and the behaviour ofthis potential and its gradient. AppendixB gives rudimentary facts about harmonicfunctions and the Poisson equation. Thesubject of Appendix C is a construction ofthe first of three comparison functions of atype introduced by D. Siegel. In AppendixD, the divergence theorem is proved.Appendix E presents the edge-pointlemma. (dm)

T. W. Gamelin, Complex Analysis,Undergraduate Texts in Mathematics,Springer, New York, 2001, 478 pp.,US$49.95, ISBN 0-387-95039-1 and 0-387-95069-9It is difficult to describe this textbook in ashort review. Among its many aims, theauthor wishes to provide beginners withstandard material in a rather flexiblecourse. About one third of material repre-sents nineteenth-century mathematics (astandard part of any basic course in com-

plex analysis); the second third, which canstill be partly covered in an undergraduatecourse, consists of selected topics such asthe Poisson integral and hyperbolic geom-etry; in the last third, the author presentstopics that have applications. The finalchapters cover the necessary backgroundfor passing PhD qualifying exams in com-plex analysis.

Surprisingly the book does not needmuch background: apart from high-schoolbasics, one needs some general under-standing of the methods of mathematicalanalysis and some knowledge of multivari-able calculus. The author considers thecourse to be a good opportunity for stu-dents to develop and consolidate previous-ly covered material, and to learn its activeuse in calculations. The preface containsuseful hints for both instructors and stu-dents. More than 800 well-chosen exercis-es with 20 pages of hints and solutions,together with clear and concise expositionsof many results, makes this book enjoyableeven for specialists in the field. The bookis recommended for libraries, students,and teachers of both undergraduate andgraduate courses. (jive)

J. J. Gray, The Hilbert Challenge, OxfordUniversity Press, 2000, 315 pp., £20, ISBN 0-19-850651-1 This book gives a fascinating account ofHilberts 23 problems, which he presentedat the International Congress ofMathematicians in Paris in 1900. Theauthor describes the life and mathematicalwork of David Hilbert (1862-1943), hisinfluence on the development of mathe-matics, and his influence on the society ofmathematicians. He describes all ofHilberts problems and shows what theywere, why they were proposed, how theyinfluenced the nature of mathematics andof mathematical thinking in the twentiethcentury, how they were solved, and so on.The reader can enjoy the reactions ofmathematicians to the Hilbert problemsand appreciate their efforts to solve them.This book is written in a clear and livelymanner, and can be recommended toeverybody interested in mathematics andmathematicians. (mnem)

E. Györi and V. T. Sös (eds.), RecentTrends in Combinatorics. The Legacy ofPaul Erdös, Cambridge University Press,2001, 192 pp., £35, ISBN 0-521-80170-2 This book is much more than just a pro-ceedings. It stems from the combinatorialworkshop, Some Trends in DiscreteMathematics, held in Mátraháza, Hungary,in October 1995. The editors have man-aged to gather surveys and research paperson the really hot topics of recent discretemathematics. The style and quality of thecontributions are such that the volume canserve as a textbook on special topics suit-able for an advanced graph theory andcombinatorics seminar, while establishedresearchers will enjoy reading many of thepapers describing recent progress in com-binatorics and giving a collection of inter-esting open problems.

The scientific quality of the book is well

complemented by its historical andhumanistic impact. The Mátraháza meet-ing was one of the last meetings in whichPaul Erdõs took part. This famous twenti-eth-century mathematician was wellknown, not only for his immense contribu-tions to mathematics (and in particular todiscrete mathematics), but also for hisunusual life style. It is very appropriatethat a volume dedicated to this unforget-table personality should be edited by hisformer students, colleagues and friends. Along foreward of over ten pages describeshis broad work in combinatorics, theimportance of his research, and his way ofthinking of mathematics as a whole. Inaddition to the professional line, the fore-word gives a rich flavour of Paul Erdõs life,with many stories that reveal his characterand help us keep in our minds a picture ofa brilliant and unique mathematician, andat the same time a warm and charitablehuman being. This book contains two con-tributions by Erdõs, one of them being thevery last paper he worked on before hepassed away in September 1996.

The topics covered in the book alsoinclude applications of algebraic tech-niques in combinatorics and graph theory in particular, polynomials and graphhomomorphisms, combinatorial numbertheory, discrete geometry and discrepancy,structural graph theory, and specialisedtopics in random graphs. (jk)

Harish-Chandra, Admissible InvariantDistributions on Reductive p-adic Groups,University Lecture Series 16, AmericanMathematical Society, Providence, 1999, 97pp., US$20, ISBN 0-8218-2025-7 The famous Harish-Chandra results onadmissible invariant distributions werepresented in Princeton in 1973, and ashort version of his lectures was publishedin his so-called Queens notes in 1978.Later, he asked P. L. Sally, Jr. to prepare adetailed version of these notes. This smallbooklet contains notes on this topic pre-pared by E. DeBacker and P. L. Sally, Jr.,which are based on Harish-Chandras ownversions of his lecture notes. The prefacealso includes comments on later develop-ment in the field, after the publication ofthe Queens notes.

The main result of the book is the factthat the character of an irreducible admis-sible representation of a connected reduc-tive p-adic group can be represented by alocally summable function on the group;the main tool used is the Fourier transformof distributions on the corresponding Liealgebra. This result by Harish-Chandrastrongly influenced the later evolution ofthe subject. It is therefore excellent tohave a carefully prepared presentation ofthis topic available in book form. (vs)

M. Kamenskii, V. Obukhovskii and P.Zecca, Condensing Multivalued Maps andSemilinear Differential Inclusions inBanach Spaces, De Gruyter Series inNonlinear Analysis and Applications 7, Walterde Gruyter, Berlin, 2001, 231 pp., DM 196,ISBN 3-11-016989-4 This monograph gives a self-contained

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presentation of the theory of condensingmultivalued (= set-valued) mappings, andapplies it to semi-linear differential inclu-sions in Banach spaces. The adjectivecondensing (with respect to a certainmeasure of non-compactness) means thatthe multivalued mapping in question doesnot increase the specified measure of non-compactness; a (regular) measure of non-compactness says, roughly speaking, howmuch a given set violates the property tobe relatively compact.

Chapter 1 summarises the basic proper-ties of multivalued mappings as far as con-tinuity and measurability are concerned.Chapter 2 then introduces abstract mea-sures of non-compactness, with specialattention to Hausdorff measure of non-compactness in separable Banach spaces(and, in particular, in spaces of continuousfunctions), and introduces basic definitionsand properties of condensing mappings.Topological degree theory for condensingboth convex-valued and non-convex-val-ued multifields forms Chapter 3; the theo-ry is briefly illustrated also by applicationsto optimal control of neutral functionaldifferential equations. Chapter 4 thengives basic facts from the theory of C0-semigroups of linear operators, with spe-cial attention to condensing operators.Measures of non-compactness in Banach-space-valued functions are also addressed.Semi-linear differential inclusions of thetype x(t) ε Ax(t) + F(t, x(t)), arising in (forexample) hybrid systems with dry frictionor in feedback control, are studied inChapter 5 (initial value problems) andChapter 6 (periodic problems). To thisaim, the multivalued part F is assumed tobe condensing with respect to a specialmeasure of non-compactness.

Reading this book from the beginning isrecommended, because there is no list ofnotation and a rather poor index. Thebook will serve excellently as a self-con-tained introductory text, as well as a state-of-art survey for researchers and advancedstudents interested in this branch of non-linear analysis. (trou)

S. Kangshen, J. N. Crossley and A. W.-C.Lun, The Nine Chapters on theMathematical Art. Companion andCommentary, Oxford University Press, 1999,596 pp., £110, ISBN 0-19-853936-3 This book is a scholarly English translationof the Chinese Nine Chapters onMathematical Art, which is considered as theEastern counterpart of Euclids Elements. Itis an anonymous text of more than 2000years old. It served as a textbook not onlyin China, but also in neighbouring coun-tries, until around 1600 when Western sci-ence was introduced. This book contains amodern translation of the text, togetherwith historical commentaries which arealso very old the best known of thesecommentaries is by Liu Hui (263 AD): theSea Island Mathematical Manual which istranslated in full in Chapter 9. The amaz-ingly complex history is told with rigourand elegance.

This book is of interest to historians ofscience and to all mathematicians interest-

ed in the origins and deeper context oftheir science. (jnes)

E. Kaszkurewicz and A. Bhaya, MatrixDiagonal Stability in Systems andComputation, Birkhäuser, Boston, 2000, 267pp., DM 168, ISBN 0-8176-4088-6 In this book, the authors discuss a specialclass of stability results for dynamical sys-tems described by a system of difference orordinary differential equations. The bookstarts with a chapter that gives an overviewof several applications where the stabilityof systems can be investigated using diago-nal-type Lyapunov functions. In the sec-ond chapter, the reader can find a thor-ough introduction to the concepts of diag-onal stability and D-stability in the frame-work of matrix theory. The next chapterdeals with certain classes of dynamical sys-tems that admit the diagonal-typeLyapunov functions and gives the basic sta-bility results. The authors discuss the casesof non-linear systems, systems continuousand discrete in time, and systems withtime-varying delays in the state. In theremaining three chapters, these methodsare applied to certain problems introducedin the first chapter namely, the problemof convergence of an asynchronous itera-tive method, stability of the neural net-works, circuits, ecosystem models andlarge-scale systems.

The book is self-contained, includes bothclassical and new results presented in anunified way, and includes a great variety ofuseful references. (jhr)

S. B. Kuksin, Analysis of HamiltonianPDEs, Oxford Lecture Series in Mathematicsand its Applications 19, Oxford UniversityPress, 2000, 212 pp., £39.50, ISBN 0-19-850395-4The aim of this book is to present the fol-lowing form of the proof of Kolmogorov-Arnold-Moser (KAM) theorem: most of thespace-periodic finite-gap solutions of aLax-integrable Hamiltonian partial differ-ential equations (PDE) persist under asmall perturbation of the equation as time-quasiperiodic solutions of the perturbedequation. This theorem provides animportant tool for an effective study ofnon-linear PDEs.

In Chapter 1, the theory of HamiltonianPDEs is developed. The presentation ofabstract Lax-integrable equations is givenin Chapter 2. The properties of classicalLax-integrable PDEs are discussed in nexttwo chapters. The following three chap-ters contain a description of normal formsfor Lax-integrable PDEs in the vicinity ofmanifolds, formed by finite-gap solutions.The final three chapters contain the proofof the main theorem. A number of techni-cal details are explained in the Addendum.

The book is devoted to global aspects ofthe KAM theorem for PDEs, and does notinclude two local theories, perturbations oflinear equations and small oscillations innon-linear equations. (pso)

P. Y. Lee and R. Výborný, The Integral:An Easy Approach after Kurzweil andHenstock, Australian Mathematical Society

Lecture Series 14, Cambridge University Press,2000, 311 pp., £24.95, ISBN 0-521-77968-5 As the title of the book suggests, theKurzweil-Henstock theory of integration isdealt with. Introductory topics are includ-ed to the first chapter, while in the second,the basic defintion of the integral is given,with its important basic properties. Moresophisticated topics are given in Chapter 3,including the convergence theorem forKurzweil-Henstock integrals, based on theconcept of equi-integrability of a set offunctions, and the McShane integral,which is equivalent to the Lebesgue inte-gral and can be also defined by usingRiemann-type integral sums for certainpartitions of an interval. In Chapters 4and 5, the strong Luzin integral is definedand is shown to be that it is equivalent tothe Kurzweil-Henstock integral. This partof the book mentions more advanced con-cepts concerning real controlled conver-gence results, including AC* and BV* func-tions, as we know them from the classicalbook of S. Saks and P. Y. Lee. In Chapter6, the integration of functions over n-dimensional intervals is presented, withFubini-type theorems and change of vari-ables (substitution). At this point, theauthors mention that, because theKurzweil-Henstock integral is a non-absolutely convergent integral, the inte-gration over n-dimensional sets causes dif-ficulties that can be overcome by lookingfor absolutely Kurzweil-Henstock inte-grable functions. The last chapter of thebook is devoted to some applications of theprevious theory to problems in analysis(line integrals, Greens theorem, Dirichletproblem, Fourier series, etc.).

The book is well written, is suitable foruse in elementary courses as well as forgraduate studies, and can be recommend-ed for a wide audience of students and spe-cialists in the theory of integration and realanalysis in general. (s)

S. Morosawa, Y. Nishimura, M.Taniguchi and T. Ueda, HolomorphicDynamics, Cambridge Studies in AdvancedMathematics 66, Cambridge University Press,2000, 338 pp., £45, ISBN 0-521-66258-3This book is a comprehensive introductionto holomorphic dynamics, induced by iter-ations of holomorphic maps. It is wellknown that even iterations of a quadraticpolynomial can produce very complicatedfractals. The first part of the book(Chapters 1-5) is devoted to dynamics ondomains in the Riemann sphere, while therest (Chapters 6-9) treats the case of twocomplex variables.

In Part I, Chapter 1 summarises thebasic facts on iterations of a polynomialnear a fixed point. A dichotomy withrespect to the dynamics of a given rationalor entire function (Fatou and Julia sets) isinvestigated in Chapter 2, where impor-tant properties of both sets are explained.Chapter 3 describes phenomena typical forentire functions. Chapter 4 starts with theNewton iterations for zeros of a meromor-phic function and continues with theFatou-Julia-Sullivan theory of iterations of

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rational functions and Shishikuras esti-mate. The last chapter of the first part isdevoted to the so-called conformaldynamics (group actions of Kleiniangroups) and to the Sullivan dictionary ofanalogies between iterations of holomor-phic functions and actions of a Kleiniangroup; this chapter also contains severalrecent conjectures related to the main one:structurally stable rational functions arehyperbolic.

Part II starts with a brief introduction tothe analysis of several complex variables.Chapter 6 explains the behaviour near afixed point (including stable and unstablemanifolds). Chapter 7 studies polynomi-als, especially complex Hénon maps. Thelast two chapters are devoted to a measure-theoretic treatment of dynamics which isbased on the so-called pluripotential theo-ry.

Since complex dynamics is a modernsubject, the book contains many recentresults. Even though the text is almost self-contained and very carefully written, thereader needs a good background knowl-edge of the classical geometric theory of acomplex variable (e.g., from Ahlforsbooks) and some experience of topologyand measure theory. (jmil)

T. W. Palmer, Banach Algebras and theGeneral Theory of *-Algebras, Vol. II: *-Algebras, Encyclopedia of Mathematics and itsApplications 79, Cambridge University Press,2001, 822 pp., £75, ISBN 0-521-36638-0This is the second volume of a two-volumeset on Banach algebras and *-algebras; thefirst volume appeared in 1994, also in theEncyclopedia of Mathematics and itsApplications series. It provides a modernaccount of basic Banach algebra theoryand deals with *-algebras.

It is difficult to describe in detail the con-tents of this voluminous monograph. Theauthor starts with a chapter devoted to *-algebras, emphasising their structure andexploring the algebraic results (*-repre-sentations, linear maps, irreducible *-rep-resentations and hermitian and symmetric*-algebras) that underlie the theory ofBanach algebras and *-algebras. The nextchapter deals with special *-algebras (G*-algebras, BG*-algebras, T*-algebras, S*-algebras, Sq*-algebras, U*-algebras, her-mitian U*-algebras and γS*-algebras). Inthe subsequent chapter the author extendsnearly all the results previously known forBanach *-algebras and hermitian Banach*-algebras (which include C*-algebras as avery special case) to *-algebras with variousalgebraic restrictions (including automaticcontinuity for Banach *-algebras andresults for Hilbert and Tomita algebras).The final chapter is devoted to locally com-pact groups (including the study of con-nected groups, Lie groups, totally discon-nected groups and group representations)and *-algebras related to them.

This second volume of the set is accom-panied by a wealth of historical remarksand examples. At the end, an extensivebibliography is attached. The volume alsocontains unpublished results with com-plete proofs at a graduate student level.

This two-volume set is recommended bothfor graduate students and experts in thefield of *-algebras. (jl)

M. M. Postnikov, Geometry VI.Riemannian Geometry, Encyclopaedia ofMathematical Sciences 91, Springer, Berlin,2001, 503 pp., DM 199, ISBN 3-540-41108-9This book is a more-or-less standard intro-duction to Riemannian geometry, includ-ing its global aspects. It has strong inter-sections with some well-known textbooks(Gromoll-Klingenberg-Meyer, Kobayashi-Nomizu, Helgason, etc.). What is non-standard here is the order of the chapters,where the really introductory chapters areput at the end of the book.

Two chapters are of particular interest:Chapter 5 about symmetric spaces, wherethe algebraic approach of O. Loos isexplained, and Chapter 24 on four-dimen-sional manifolds, which is a real master-piece that includes many global results.Many interesting and non-trivial exercisesare included in every chapter.

On the other hand, this monograph hassome weaknesses. First, even though theauthor refers to many famous namesthroughout the book, he never gives stan-dard references: instead of usual list of ref-erences he gives only a short list of sug-gested reading at the end of the book.This seems rather unusual for an encyclo-pedia book. Secondly, in some places, theinformation is so fragmentary that itbecomes useless. For instance, on page 54there is a special paragraph called Semi-symmetric spaces, which includes only adefinition and the trivial statement that alllocally symmetric spaces are semi-symmet-ric. Perhaps the author has no idea aboutthe recent developments in this highlynon-trivial topic, starting with the funda-mental paper by Z. Szabó (J. DifferentialGeometry, 1982). This paper shows, in fact,that the locally symmetric spaces form asubset of measure zero in the class of allsemi-symmetric spaces. (ok)

H. Reiter and J. D. Stegeman, ClassicalHarmonic Analysis and Locally CompactGroups, London Mathematical SocietyMonographs New Series 22, Clarendon Press,Oxford, 2000, 327 pp., £60, ISBN 0-19-851189-2.The original book, Classical harmonic analy-sis and locally compact groups, by H. Reiterappeared in 1968. Reiter died in 1992,and his former student Jan Stegeman wasasked by Oxford University Press to pre-pare a new edition. He decided to stayclose to the original text whenever possi-ble, but nevertheless, the new edition hasexpanded and additional material hasbeen appended.

The text starts with classical harmonicanalysis (Fourier transforms, the Wienerapproximation theorem, and subalgebrasof L1(Rn)). The next chapter introducescertain topological algebras (Wiener alge-bras) and an abstract version of the Wienertheorem; Ditkin sets, ideals in functionalgebras and sets of spectral synthesis arealso studied. The next chapter concerns

the Haar measure on locally compactgroups, algebras L1(G), L∞(G) and Beurlingalgebras. The fourth chapter deals withlocally compact abelian groups and theirduality theory. Further chapters are devot-ed to functions on locally compact abeliangroups, an extension of the Wiener theo-rem for groups, and Segal algebras. Thenotion of the spectrum of a bounded mea-surable function and its properties areexplained in Chapter 7. The final chapterdescribes functions on general locally com-pact groups, including the Mackey-Bruhattheorem on the existence of quasi-invari-ant measure. The appendix containsproofs of the Domar and Malliavin theo-rems, additional material on Segal alge-bras and the notion of difference spec-trum. The book ends with notes and addi-tional references to each of the chapters.

The monograph is designed to serveboth as a general survey and as a detailedexposition of the topics it treats. It shouldbe accessible to graduate students andresearchers interested in harmonic analysisand understandable with a basic knowl-edge of functional analysis and measuretheory, together with a background of realand complex analysis. (jl)

J. Rossmann, P. Takáè and G.Wildenhain (eds.), The MazyaAnniversary Collection, Vols. 1, 2, OperatorTheory Advances and Applications 109, 110,Birkhäuser, Basel, 1999, 364 and 352 pp.,DM 238 and 238, ISBN 3-7643-6203-0 and3-7643-6202-2 The contributions to these volumes arededicated to V. G. Mazya, and are partlybased on talks given at the conferenceFunctional Analysis, Partial DifferentialEquations and Applications held inRostock in September 1998. Vladimir G.Mazya is the author and co-author of morethan 300 publications and more than adozen books, and he made significant con-tributions to many fields of mathematics,extending to the theory of Sobolev spaces,capacity theory, boundary integral meth-ods, qualitative and asymptotic methods ofanalysis of linear and non-linear ellipticboundary value problems, the Cauchyproblem for elliptic and hyperbolic equa-tions, the theory of multipliers in spaces ofdifferentiable functions, maximum princi-ples for elliptic and parabolic systems, andboundary value problems on domains withsingularities.

A major part of the first volume consistsof four surveys of his work in various fieldsof mathematics, while other articles in thisvolume have their origin in his joint workwith their authors. The first contribution,by L. I. Hedberg, deals with Mazyas earlyresults in the theory of function spaces,potential theory and partial differentialequations, including his counter-examplesto the regularity theory, which in a sub-stantial way extend the results of E. DeGiorgi and E. Giusti, and M. Miranda. Inthe second survey article, N. G. Kuznetsovand B. R. Vainberg discuss results concern-ing the unique solvability of two funda-mental problems of steady-state surface-wave theory: the problems of time-har-

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monic water waves and of a wave patterncaused by a body in uniform forwardmotion in calm water. In the third part, J.Elschner describes Mazyas work on inte-gral and pseudodifferential operators,while in the fourth, J. Rossman reviewsMazyas results in the theory of boundary-value problems on non-smooth domains;the domains considered here can havepoint singularities, edges or polyhedralvertices. The contributions based on jointwork with V. G. Mazya include paperswritten by V. Havin, G. Schmidt, R. Cooke,A. Grigoryan and T. Shaposhnikova.

The second volume contains most of theinvited lectures, as well as a few con-tributed papers. There are nineteen con-tributions, ranging from function spaces(the Hardy inequality, maximal operatorsand multipliers in Lizorkin-Triebel space),via the qualitative theory of differentialequations (maximum and anti-maximumprinciples for certain classes of systems,perturbation of trajectory attractors fordissipative hyperbolic equations, and sym-metry and asymmetry of positive solutionsto a class of semilinear equations), thespectral theory of differential operators(eigenfrequencies of fractal drums and thediscreteness of the spectrum for theSchrödinger operator on certain mani-folds) to results coupling a continuousdescription with discrete models andnumerical results (coupling of finite andboundary element methods for the time-harmonic Maxwell equations, and hybridmethods for boundary value problems viaboundary energy).

This is a useful publication giving a goodoverview and many interesting results inthis vast field. (jsta)

C. Sabbah, Equations différentielles àpoints singuliers irréguliers et phénomènede Stokes en dimension 2, Astérisque 263,Société Mathématique de France, Paris, 2000,190 pp., FRF 150, ISBN 2-85629-085-X The study of systems of linear differentialequations in one complex variable arounda singular point is an old classical subjectthat goes back to Riemann and Fuchs. Inthe case of a regular singularity (the Fuchscondition), the solutions have at most poly-nomial growth near the singularity. Thehigher-dimensional analogues of equa-tions with regular singularities are welldeveloped using the language of flat con-nections on vector bundles, and far-reach-ing beautiful generalisations of classicalresults are available describing the appro-priate Riemann-Hilbert correspondence.

The situation is much more complicatedin the case of equations with irregular sin-gularities. This case includes a lot of inter-esting examples, such as the Bessel equa-tion, the Whittaker equation, the Airyequation, and many others. The solutionsof such equations no longer have polyno-mial growth near the singularity, and for-mal solutions are almost always divergent.Analytic solutions are defined only in a sec-tor with its vertex at the singularity point,and their asymptotic relation to formalsolutions changes when the boundary ofthe sector crosses the so-called Stokes

lines. Such a Stokes phenomenon is adeep-lying characteristic of the given dif-ferential equation. A quite complete theo-ry is available in the case of one variable.

The topic treated in the book is theasymptotic theory of holonomic linear dif-ferential equations for two complex vari-ables with irregular singularities. Theproblem is formulated in the language offlat connections for a meromorphic vectorbundle on a complex analytic surface. Inthe first chapter, the key notion of a goodformal structure for a meromorphic vectorbundle with a flat connection is introducedand discussed. The second part is devot-ed to a study of the Stokes phenomenonfor connections that admit a good formalstructure. The third part of the book stud-ies analogues of Turrittins theorem fromdimension 1, concerning the existence of agood formal structure for a meromorphicconnection (on the pull-back by a sequenceof complex blowing-up) and their conse-quences. The existence proof is given forbundles of rank at most five. Throughout,the author freely uses the modern lan-guage of sheaves, D-modules and corre-sponding functors.

The book presents a systematic treat-ment of the results published orannounced by the author in the last tenyears. (vs)

P. L. Sachdev, Self-Similarity and Beyond.Exact Solutions of Nonlinear Problems,Monographs and Surveys in Pure and AppliedMathematics 113, Chapman & Hall/CRC,Boca Raton, 2000, 319 pp., £63.99, ISBN 1-58488-211-5As its title suggests, the main aim of thismonograph is to find exact solutions forproblems described by non-linear partialdifferential equations (PDEs). For thispurpose, several techniques and approach-es are considered. Starting from self-simi-lar transforms that are useful in finding theasymptotic behaviour of solutions, a con-struction of a blow-up solution and a betterunderstanding of the structure of the prob-lems, the author presents the systematicgroup transform approach and the directClarkson-Kruskal method for finding suchself-similar solutions, and also providessuch further techniques as travelling wavesolutions, exact linearisation (as the hodo-graph method) of non-linear partial differ-ential equations, the infinite seriesmethod, and embedding special solutionsinto a more general class in order to obtainsolutions of non-linear PDEs of a moregeneral character than self-similar ones.The methods iand their limitations areclearly explained, and are complementedby a number of solved examples focusingon equations in fluid mechanics and non-linear diffusion. (jmal)

J. L. Schiff, The Laplace Transform:Theory and Applications, UndergraduateTexts in Mathematics, Springer, New York,1999, 233 pp., DM 79, ISBN 0-387-98698-7The book introduces the Laplace trans-form and the related complex variable the-ory in a beautiful, pedagogical and rigor-

ous way. Through a large number ofexamples and exercises, it is shown thatthe Laplace transform is an extremely use-ful tool in solving linear problems, includ-ing ordinary differential equations withconstant coefficients or time delay, or time-dependent coefficients, integro-differen-tial equations, difference and partial dif-ferential equations, and problems withDirac distribution (via the Riemann-Stieltjes integral). All assertions areproved.

This clearly written undergarduate text-book can be recommended to students andteachers of this subject, both in a mathe-matical and engineering context. (jmal)

J. C. Simo and T. J. R. Hughes,Computational Inelasticity, Interdisci-plinary Applied Mathematics 7, Springer, NewYork, 1998, 392 pp., DM 129, ISBN 0-387-97520-9This book deals with numerical simulationfor classical non-controversial elastoplas-ticity models, avoiding any problems aris-ing from pattern formation or materialinstabilities. However, large-strain elasto-plasticity is covered. The ideas of linearelastoplasticity are clearly explained, firstin one-dimensional setting. Then themodels are generalised to three dimen-sions. This is followed by a very clear anddetailed explanation of time (backwardEuler) and finite element (mixed formula-tion for displacements, stresses and strains)discretisations. Next, the authors proceedto large-strain models and their numericalapproximations, completed by numericaltests. This is followed by the objectivefinite-difference approximations of theframe-invariant time derivative of tensors.Finally, linear viscoelasticity models aretreated.

This book is well written, is easy to fol-low, and contains much useful material forresearchers and graduate students in vari-ous branches of engineering and appliedmathematics. (jmal)

C. Truesdel and K. R. Rajagopal, AnIntroduction to the Mechanics of Fluids,Modeling and Simulation in Science,Engineering and Technology, Birkhäuser,Boston, 2000, 277 pp., DM 148, ISBN 0-8176-4012-2 and 3-7643-4014-2 This textbook acquaints the reader withcontinuum equations of fluid motions, inan elementary but precise way. Theauthors restrict themselves to isothermalprocesses. Although compressible Eulerequations are also treated, the mainemphasis is on incompressible fluids: thebook deals with general simple fluidsunder the incompressibility constraint, thelinear (Navier-Stokes) fluid, the inviscid(Euler) fluid, and some second- and third-degree examples of non-linear fluids. Theequations are correctly derived and enor-mous simple flows for these fluids areintroduced, computed and analysed.Among other topics, monotonous motions,viscometric flows, and flows in simplegeometries (both steady and unsteady) areconsidered. Each section contains severalvaluable exercises; readers can verify their

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solutions with those provided in an appen-dix.

This book will be appreciated by thosedesiring a better understanding of fluidmotions. (jmal)

J.-L. Waldspurger, Intégrales orbitalesnilpotentes et endoscopie pour les groupesclassiques non ramifiés, Astérisque 269,Société Mathématique de France, Paris, 2001,449 pp., FRF 400, ISBN 2-85629-096-5Let F be a finite extension of Qp, let G bean unramified classical group (orthogonal,symplectic or unitary) over F, and let g bethe Lie algebra of G. Denote by DG

nil thespace of invariant distributions supportedin the nilpotent set on g(F), and by DG,st thespace of stably invariant distributions ong(F). Let H be an elliptic unramified endo-scopic group of G. The main results ofthis work (assuming that p is large enough)are an explicit description of the intersec-tion of DG

nil and DG,st, and an explicitdescription of the transfer map from theintersection of DH

nil and DH,st to DGnil. The

proofs use earlier results of the author,relating DG

nil to distributions with integralsupport, and detailed calculations basedon the Springer correspondence and theLusztig Fourier transform. (jnek)

R. Wilson and J. Gray (eds.),Mathematical Conversations. Selectionsfrom the Mathematical Intelligencer,Springer, New York, 2001, 488 pp., DM 119,ISBN 0-387-98686-3This book contains forty articles that werepublished in The Mathematical Intelligencerduring its first eighteen years. The editors

have chosen a wide selection of articles, soas to present the most important and sur-prising mathematical ideas. The articlesare divided into seven groups.

The first part, Interviews andReminiscences, contains two interviews withleading figures from todays mathematics,three reminiscences and memoirs, and onearticle with mathematical anecdotes. Thesecond part, Algebra and Number Theory,shows in six articles some of the mostimportant and significant problems in thefield (for example, the proof of theMordell conjecture, the representationtheory of finite groups, and quaternionicdeterminants). The third part, Analysis,also has six articles, describing some inter-esting discoveries (including the Banach-Tarski theorem, Painlevés conjecture anda geometrisation of Lebesgues space-fill-ing curve). Five articles in the fourth part,Applied Mathematics, demonstrate thatphysics remains at the core of appliedmathematics; in particular, a combinationof interesting topics and new kinds ofmathematics contribute to the currentrevival of applied mathematics. The fifthpart, Arrangements and Patterns, containsfive articles devoted to questions of collab-oration between modern artists and math-ematics; here, readers can enjoy a richmixture of mathematical, artistic and cul-tural themes, including articles on Celticknotwork, mathematical art, and the pave-ment of the Baptistery of San Giovanni inFlorence. The sixth part, Geometry andTopology, explains in six articles some ofthe most famous discoveries since the1960s (instantons and the topology of 4-

manifolds, the computer-aided discoveryof new embedded minimal surfaces, hyper-bolic geometry, and moduli spaces ofRiemann surfaces). The final part, Historyof Mathematics, includes six articles thatdescribe the everyday life of mathemati-cians (their lives, work, interaction, andcollaborations); these articles are devoted(for example) to Kurt Gödel, Hilbert andBrouwer, and the history of the Bieberbachconjecture. (mnem)

List of reviewers for 2001The Editor would like to thank the following fortheir reviews this year:

J. Andìl, J. Antoch, M. Nìmcová-Beèváøová,L. Bican, M. Brzezina, J. Bure, E. Calda, M.Dont, A. Drápal, J. Dupaèová, A. Elashvilli, E.Faangová, M. Feistauer, T. Fürst, J. Hron, M.Huková, V. Janovský, J. Jeek, O. John, A.Karger, J. Kofroò, O. Kowalski, J. Kratochvíl,P. Kùrka, P. Lachout, M. Lichá, J. Luke, J.Málek, J. Malý, M. Markl, J. Matouek, D.Medková, J. Milota, J. Mlèek, K. Najzar, J.Nekováø, J. Neetøil, I. Netuka, B. Novák, .Porubský, D. Praák, P. Pyrih, M. Rokyta, T.Roubíèek, . Schwabik, J. Slovák, P. Somberg,V. Souèek, J. Stará, Z. ír, J. tìpán, J. Trlifaj,V. Trnková, J. Tùma, J. Vanura, J. Veselý, J.Vybíral, M. Zahradník, K. Zimmermann.

All of these are on the staff of the CharlesUniversity, Faculty of Mathematics andPhysics, Prague, except M. Markl, D. Medkováand J. Vanura (Mathematical Institute, CzechAcademy of Sciences), M. Nìmcová-Beèváøováand . Porubský (Technical University,Prague), J. Nekováø (Cambridge University,England) and J. Slovák (Masaryk University,Faculty of Natural Sciences, Brno).

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