MAIN CHARACTERS AT ICM 2006

John Morgan: “In the mathematical context Perelman was forthcoming and patient”

John Morgan (ColumbiaUniversity, New York, USA,together with Gang Tian(Princeton University, USA),has written a book presenting acomplete account of the proofof the Poincaré Conjecturebased on Perelman’s ideas.Morgan gave a pressconference yesterday at theICM2006. This is atranscription of his answers.

About his lecture at theICM2006, entitled “SpecialLecture on the PoincaréConjecture”.

“Perelman’s work is anextraordinary achievement. Inthe last hundred years we havelearnt so much about topologyand as a result of that knowledge somebody with theinsight and technical power of Perelman could finish offthis fundamental problem. It’s a great success.

“Mathematics is a discipline in which there are veryhard problems that you don’t know how to solve, but ifyou study more and more you can get slowly a deeperand deeper understanding. This is what has happenedwith the problem of the Poincare conjecture. Toparaphrase Newton, Perelman has seen far, but in order todo that he has stood on the shoulders of giants. Andcertainly one giant who stands out is Richard Hamilton,who painstakingly over 25 years developed the basic ofthis theory [the Ricci flow] and laid the foundation forPerelman’s work.

Ar e you satisfied with the work of Perelman, is therea consensus in the community about the proof thePoincaré Conjecture?

Gang Tian and I have written a paper of 473 pages onwhat we consider a complete revision of the proof of thePoincaré Conjecture: this is the result of several years inwhich I tried to understand Perelman’s arguments. And asevery professor of mathematics knows, if you want tolearn a subject, teach it. At the end of that experience Iam really convinced that the Poincaré Conjecture isproved. (...) There are also two other really long articlesby Zhu and Cao and another one by Kleiner and Lottgoing over much the same terrain. And yes, I would saythat at that point you have a consensus among the peoplewho have seriously studied Perelmans’preprint and

Hamilton’s work that theconjecture has been proven.

About the paper by Xi-PingZhu and Huai-Dong Cao, andthe controversy about theauthorship of the solution ofthe problem.

To me all three of these papersplay a similar role but notexactly the same... but all ofthem have to be viewed asunpacking, expanding on, fillingin missing details. I am not anexpert on either of the other twoarticles because I was so busywriting my own. But I certainlydon’t see major significantcontributions independent ofwhat Perelman has done. Andafter looking the paper by Zhu

and Cao it seems to me an honest account with theappropriate credit all the way through, and all thecontroversy stems not from this paper but from the noisearound it.

About the differences between the three publicationson Perelman’s work

Our work is more different from the other two thanthey are from each other. The main difference is wefocus only on the Poincaré Conjecture, while thosearticles discuss the more general geometrizationconjecture, and the arguments take different paths. Themain body of all three treat the same subject, which isthe existence of the Ricci Flow with surgery. If you wantto prove the Poincare Conjecture only, which is what wechose to do, there is a third pre-print by Perelman, andwe followed that argument because we thought it was abeautiful argument on its own, both Kleiner and Lott andCow and Yow do not treat that third Perelman paper, butrather follow the suggestion at the end of the secondpaper, which deals mostly with the geometrizationconjecture.

Is Perelman’s proof complete?I believe if you take all three papers by Perelman

together they are 55 or 60 pages, and we wrote 473pages. The first hundred pages were mostly backgroundinformation and the rest was mostly unpacking and re-ordering what was contained in the 55 pages of Perelman.I think that Perelman was writing for experts in the field.We are writing for graduate students.

Morgan at yesterday´s press conference

I C M 2 0 0 6Daily News

Madrid, August 25th 2006

Transcription of the press conference held on the 24th of August

The experience I have had multiple times when readingPerelman is that I would read something and I wouldn’tunderstand a word of it. Then I go home and think aboutit. If I didn’t understand it I would talk to Tiang about it,to Hamilton... When I eventually understood it –hourslater, days later, sometimes weeks later—I would askmyself, OK, if I had to explain its main points as a guidein one paragraph what would I do? So having had thatexperience over and over again and never finding that theparagraph that Perelman wrote deviated from anabsolutely accurate if incredibly compressed descriptionof the argument that I had understood to be completelycorrect, I conclude that Perelman had just decided forsome reason to compress everything.

In r elation to the sentence in the abstract of thepaper by Zhu and Cao, where they talk about the“Perelman-Hamilton” pr oof of the PoincaréConjecture.

“I guess that is their view of it”Can we say that Perelman has proven the Poincaré

Conjecture?Yes, I would say and I will say today that Perelman has

proven the Poincaré Conjecture. But one has tounderstand that he would not have done it withoutHamilton’s work. Yet, in the culture of mathematics it ismy view that the credit for proving the PoincaréConjecture should go to Perelman.

What will change in the field after thedemonstration of the Poincare Conjecture?

In some sense nothing will change. In the work in 3Dtopology the state of the art will not change (...) . Thesignificance is the understanding of these evolutionequations, the Ricci Flow equations and the way theydevelop singularities. This will have applications in othermathematical areas (...). And a little more speculative, theway these evolution equations develop singularities isincredibly important within mathematics and in physicalphenomena. Many, many physical phenomena areexplained by evolution equations similar to the RicciFlow, so understanding the way these equations developsingularities, and how to treat these singularities, havetremendous consequences inside mathematics andphysical sciences.

Have you met Perelman?I met him when he made his tour to the United States in

2003, when he came to explain his ideas. I attendedseveral of his lectures and then talked privately with himon several occasions, and after he went back to Russia Iwas in e-mail contact with him when I was struggling tounderstand his writings. And he was always veryforthcoming and patient in explaining his ideas, so whilehe seems to be socially reclusive, in the mathematicalcontext he was forthcoming and patient.

Would you say he is a genius?I don’t use words like that. He is an incredibly talented

and insightful and powerful mathematician. What he hasmanaged to do is a reflection of incredible power. I justdon’t find use in that kind of word.

How did you experience the controversy around theauthorship of the demonstration of the Conjecture?

I was mostly focused on trying to be in the position Iam today, sitting in front of you and saying that Perelmanproved the Poincare conjecture, so I was very focused onhaving this 473 pages completely written and makingsure that I completely understood the arguments entirely.I was of course aware of what happened, but I wanted tostay focused.

What was the key point in Perelman’s argument?What was it that Hamilton didn’t see?

Hamilton knew that you had to study singularitydevelopment, and he proved several important propertiesabout the way singularities develop. But he missed one.Perelman realised that this extra property, neverconsidered by Hamilton, was in fact essential. Hamiltonhad one singularity; he was very worried about he calledthe cigar. And what made everyone sit down and takenotices was that he established that the cigar couldn’thappen. And that was a real problem in Hamilton. SoPerelman added a new condition on top of the others thatHamilton had discovered, for the way singularitiesdevelop. He recognised that this was an importantcondition and by a completely different technique, unlikeanything in Hamilton, established this condition. Andthen he went on to establish that he had very powerfulcontrol of the way singularities develop, which enabledhim to do the kind of surgery that Hamilton had proposeddoing but couldn’t always carry out. That to me is themost original insight.

But Perelman also had the incredible technical power totake the tools that Hamilton designed and use them in aneven more subtle way to understand not only what onesingularity was but to control them all.

Will the Poincaré Conjecture now change its nameto Poincare’s Theorem.

I believe it will always be the Poincaré Conjecture. Tome the statement that Perelman has solved the PoincaréConjecture means Perelman has turned the PoincaréConjecture into a theorem. But we will still talk about thePoincaré Conjecture, because the name is deeply involvedin mathematics.

But everyone will think that it is now a theorem...I hope so! I hope everyone will read the 1000 pages

and say, of course! Should Perelman get the millennium prize of the

Clay Foundation?Unfortunately that is not for me to say. You must have spent an incredible amount of time

on it.I was motivated by three things. One is: I am a

topologist, and here is a solution to the most fundamentalquestion in the subject, how did this guy do it? I wantedto understand for myself. And when I started tounderstand the arguments I was more and more impressedwith the beauty of the argument. That was my secondmotivation. Also, my third reason was to make a serviceto the community, I didn’t want the topologists not to beable to understand such a beautiful argument. Of coursehad I known how much work was really involved, Imight have taken a different path two years ago!

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These days the name “Nevanlinna” is virtuallysynonymous with that of the North Americanmathematician Jon Kleinberg (Cornell University, USA),the latest winner of this prize, which is awarded everyfour years for advances in computer science and theInformation Society. Thus the conversation quickly turnsto subjects such as electronic business, new kinds of on-line economics, the interconnected world and the qualityof information on the Net, absolutely vital in anincreasingly computerized society. Kleinberg reflects onthese subjects from a mathematical point of view, sincemathematics is the tool he employs for creating modelsbased on probability theory; models which in a certainsense he uses in order to understand human behaviour.“Sometimes it seems as though computers can think”,says Kleinberg, “but they only process data. That’s whyit’s interesting for us to analyze how we use them,because in the end they are only intermediaries betweenpeople. Understanding how we work with computersgives us valuable information; because texts, forexample, are like people. If we apply probability to thesedocuments, we find mathematical models that provide uswith interesting data, information with an economic valuethat tells us about human behaviour, habits, tastes, andways of thinking”.

For Kleinberg, the way we organize and structureinformation is vital, and from here to an efficient andstructured web-search is the step where he appliesprobability theory. His aim – to make navegating on theWeb more effective. Kleinberg has developed amathematical model for making searches for informationon Internet or in email in-trays more intelligent. A web-search can be carried out in two ways; a libraryconsultation, so to speak, in which the user asks themachine for all the material concerning a particularsubject; and a second, more intelligent way that detectswhen an event has made the news, and is therefore ofgeneral interest. To make this second method fullyworkable, Kleinberg detects the most frequently repeatedwords in a given text and assigns a value to certain keywords so the computer can indicate if the text ordocument in question contains anomalies. “This is amathematical model that assigns a value to each worddepending on its level of interest”, explains Kleinberg.Thus, for example, in an analysis of speeches by USPresidents over 200 years, Kleinberg has found certainwords referring to special events that have made news. Ingraph form, it would look like this: on the vertical axiswe put the number of times a certain word – for example,“Vietnam” - is used. On the horizontal axis we put atimetable in years (i.e. 1800, 1850, 1900, 2000). Such agraph would very quickly reveal that beginning in 1950something very significant occurred in the relationbetween US politics and Vietnam. If the word selectedwere the definite article “the”, the line on the graphwould be flat and unbroken, indicating nothing worthy ofmention. This news-based way of scanning texts wouldalso reveal, for example, that in Madrid something

John Kleinberg: “Texts are like people”

unusual occurred in March, 2004. Let us imagine a readerusing a search engine to find information about Madrid.The library-type consultation would provide all types ofreferences to the city (museums, monuments, history ofthe city, news, etc.). The news-based search, on the otherhand, world quickly show us that on March 11th, 2004,something unusual and unexpected happened in theSpanish capital. This would be reflected by thecomputation of references rising from 0 to x on thevertical axis, without an ascending curve, peak ordescending curve, which would occur with a predictableevent such as a general election. This same technique canbe applied to electronic mail. “My emails are veryboring,” says Klienberg. “They’re all about work.However, thanks to this method and can select or searchfor what interests me and check what I’ve been workingon”. When asked what would be the key words forunderstanding his way of thinking, those that mostfrequently appear in his emails, Kleinberg repeats thatthey’re all about work, although he points out a practicalapplication. “I’ve managed to search for names of friendswho I hadn’t seen for six years and with whom I’d lostcontact by asking the machine for search patterns”, heexplains, “and it was able to tell me we had a relationsome years ago. These peaks appeared as frequentinformation”.

In answer to whether we will soon have a search enginethat thinks like a human being, Nevanlinna award-winnerKleinberg replies in the negative. “There’s nothing moreenriching than speaking directly with an expert if youwant to understand something. There’s still no way ofreading, seeing or assimilating knowledge that beatsspeaking face to face with someone, without machines inbetween”

Kleinberg also draws attention to how much the spreadof PC use has changed society in the last 15 years.

“Computers are creating a new world, and in this virtualspace the rules are much more flexible. In physics therules are golden, but not here. The Web constitutes a newway of thinking”. In this sphere, information, and how itis organized, are becoming increasingly important. Butthere are no fixed rules. For example, Kleinberg’s methodcould not be used to determine the quality of informationin a blog. “Now [that everyone can publish] the validinformation is that with a reputation. And how do weknow when the source is reputable?” asks Kleinberg. Theanswer, he adds, is its level of accuracy, a quality thatcomputers are unable to judge. “But we know,” saysKleinberg, “just as we know what newspapers arereputable, who produces them and weighs theinformation”. A blog may have as many as 200 readersevery day, but that

Kleinberg also draws attention to how much the spreadof PC use has changed society in the last 15 years.“Computers are creating a new world, and in this virtualspace the rules are much more flexible. In physics therules are golden, but not here. The Web constitutes a newway of thinking”. In this sphere, information, and how itis organized, are becoming increasingly important. Butthere are no fixed rules. For example, Kleinberg’s methodcould not be used to determine the quality of informationin a blog. “Now [that everyone can publish] the validinformation is that with a reputation. And how do weknow when the source is reputable?” asks Kleinberg. Theanswer, he adds, is its level of accuracy, a quality thatcomputers are unable to judge. “But we know,” saysKleinberg, “just as we know what newspapers arereputable, who produces them and weighs theinformation”. A blog may have as many as 200 readersevery day, but that does not mean that the informationone finds there is trustworthy. “That’s why,” saysKleinberg, “one can predict whether a newspaper willcontain accurate information or not – because itsreputation depends on it”

HIGHLIGHTS OF JON KLEINBERG´SWORK

Jon Kleinberg’s work has brought theoretical insights tobear on important practical questions that have becomecentral to understanding and managing our increasinglynetworked world. He has worked in a wide range ofareas, from network analysis and routing, to data mining,to comparative genomics and protein structure analysis.In addition to making fundamental contributions toresearch, Kleinberg has thought deeply about the impactof technology, in social, economic, and political spheres.

One of Kleinberg’s most important researchachievements focuses on the network structure of theWorld Wide Web. His insights have greatly influencedhow all of today’s major search engines operate. Whileindividual web pages have a degree of structure imposedby the creators of those pages, the structure of the WorldWide Web as a whole is completely unplanned; the

structure is continually emerging as new content and linksare added. As a result, it is a challenging problem todesign effective ways of selecting relevant web pages tooffer to search-engine users. Prior to Kleinberg’s work,search engines focused only on the content of web pages,not on the link structure. In 1996, Kleinberg introducedthe idea of “authorities” and “hubs”: An authority is aweb page that contains information on a particular topic,and a hub is a page that contains links to manyauthorities. For example, consider the search query“digital camera”. A web site offering guides and reviewsof digital cameras would be a hub, and the web site of amanufacturer of digital cameras would be an authority.Although the idea of hubs and authorities is clearintuitively, defining these notions mathematically isdifficult because of the circularity that arises: A hub is asite that points to many authorities; an authority is a sitewith links from many hubs. Kleinberg’s key contributionwas to figure out a way to break this circularity, therebyopening the way for a mathematical analysis of the linkstructure of networks. He developed algorithmic tools forthis problem and demonstrated their effectiveness bytesting them on the World Wide Web.

Another area in which Kleinberg has made fundamentaladvances is in that of “small-world” networks. Thesenetworks were first noticed in experiments carried out inthe 1960s by the psychologist Stanley Milgram andbecame the focus of a series of mathematical modelsbased on work of Duncan Watts and Steve Strogatz in the1990s. In Milgram’s experiments, a person A would beasked to forward a letter to person B, whom A does notknow personally, in as few steps as possible. Each personin the chain could forward the letter only to someone heor she knew personally. Milgram observed that onaverage the letter would reach B after being forwarded by6 people (this is the origin of the phrase “six degrees ofseparation”). The number 6 is surprisingly small, giventhe size of the population overall, and given that eachperson operated on the basis only of local informationabout the social network. Up through the 1990s, therewas a good deal of research in the social science literatureabout the existence of short paths between individuals insocial networks. But there was little consideration of howto find short paths given only local information. How dopeople who know only their immediate friends and do nothave a a global view of the whole network find shortestpaths? It is this question that Kleinberg addressed, and hefound some surprising things.

The nodes of a social network are the people in it; twonodes are connected if the two people know each other.Kleinberg observed that in small-world networks theprobability two nodes will be connected decreases as thegeographical distance between them increases. And heshowed that, if the probability of a connection betweentwo nodes in a network decreases with the square of thedistance between them, then there are efficient algorithmsfor finding the shortest path between the two nodes. Mostsurprisingly, he showed that if the decrease is faster orslower than the square of the distance, no efficient

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algorithm exists. In addition to elucidating theoreticalaspects of small-world networks, Kleinberg’s work hasproven useful in designing peer-to-peer file sharingsystems, where information has to be located without acentral index.

One of Kleinberg’s early results also concernedefficient algorithms, this time for the problem of finding“nearest neighbors” in high-dimensional data sets. Thisproblem arises in the following kind of setting. Supposeyou have a set of documents and a dictionary of n words.For each document, you count the number of times thefirst word in the dictionary appears, the number of timesthe second word appears, the number of times the thirdword appears, and so on. In this way you obtain n counts,and they can be thought of as an n-dimensional vectorthat represents the document. For any particulardocument A, how can you identify its nearest neighbor—-that is, the document B that is the most similar to A of allthe documents in the set? Thinking of A and B as vectors,you want to find B such that the distance from A to B isas small as possible. One solution is of course to simplycompute the distance between A and every other vectorand then see which distance is smallest. But if n—-thenumber of words in the dictionary—-is very large, thenone is dealing with a very high-dimensional space. Inhigh-dimensional spaces the brute-force technique ofsimply checking all the possibilities runs quickly into the“curse of dimensionality” and becomes time-consumingand expensive. Kleinberg broke this impasse bydeveloping an ingenious new approach to the nearestneighbor problem, by randomly combining one-dimensional projections of the vectors.

Another highlight of Kleinberg’s work is hisdevelopment of a mathematical model to recognize“bursts” in data streams. One way of analyzing thestructure of information contained in a text data stream isto look for bursts of activity that appear suddenly and aresustained for a period of time. For example, even if youdid not speak English, if you observed the sudden andfrequent appearance of the word “Katrina” in news wiredata from August 2005, you would know that somethingsignificant was happening. Kleinberg began studyingbursts for a very practical reason: He wanted a better wayof organizing the huge archive of personal email that hewas accumulating. While the idea of a burst ofinformation activity is intuitively clear, defining thenotion rigorously is not easy, because of the difficulty ofdistinguishing bursts from statistical fluctuations in a seaof random information. Kleinberg’s key contribution wasto supply such a rigorous definition of bursts, using themathematical concept of Markov models. He tested hisideas on a range of different data sets, such as the titles ofresearch papers spanning several decades of research in agiven area. In this case, the bursts correspond to theappearance of and attention paid to new topics in thatresearch area.

The interplay between understanding networkstheoretically and observing actual networks in action hasinformed Kleinberg’s research and brought new

perspectives about the role of technology in society. “TheInternet and the Web force us to think about the socialconsequences of a world in which information is moreplentiful and travels more widely than ever before, and inwhich anyone has the potential, through new kinds ofmedia and at very little cost, to become an author with aglobal audience,” Kleinberg wrote in an email interviewconducted with Technology Research News onlinemagazine. “But there are a number of fundamentalchallenges here. We know that on-line discourse can behighly polarized; is it the case that the on-line tools we’vecreated are contributing to a rising level of polarization incivic dialogue more generally? How might we accuratelyassess this phenomenon, and how might we think aboutdesigning new tools that make on-line discourse moreproductive?”

Kleinberg’s work is distinguished by its richness anddiversity, and also by his ability to use theoretical insightsand deep understanding to address practical problems.This powerful combination ensures Kleinberg’s status asone of the leading thinkers in theoretical computerscience in the years to come.

BIOGRAPHICAL SKETCHJon Kleinberg was born in 1971 in Boston,

Massachusetts, USA. He received his Ph.D. in 1996from the Massachusetts Institute of Technology. He is aprofessor of computer science at Cornell University.Among his distinctions are a Sloan FoundationFellowship (1997), a Packard Foundation Fellowship(1999), and the Initiatives in Research Award of the U.S.National Academy of Sciences (2001). In 2005,Kleinberg received a MacArthur “genius” Fellowshipfrom the John D. and Catherine T. MacArthurFoundation.

by Allyn Jackson(also author of yesterday’s Highlights of Tao’s Work)

Kleimberg receiving his prize

“Demoscene”:from computerpiracy to art6 ICM 2006 MADRID SPAIN

It all began as a hobby, an urban subculture, acompetition among programmers for cracking softwareprogrammes and videogames, and now it has become away of investing the mass of microchips we work withevery day with the spirit of art. “Demoscene” is acomputer art form for creating animated images, usuallywith music, using programmes that run in real time. Aprofound knowledge of mathematics and geometry lies

behind its development. Inorder to see, understand andeven participate in whatdemoscene is all about, onecould not do better than visitthe exhibition at the CentroCultural Conde Duque (CondeDuque Cultural Centre) inMadrid from August 17th toOctober 29th. The exhibition isone of the cultural eventsrunning in parallel with theICM2006 InternationalCongress of Mathematicians,and its success caused RaúlIbáñez, curator of theexhibition, to say: “I’ve neverseen people queuing for aMaths Exhibition before!”. Alive demonstration ofdemoscene took placeyesterday at the PalacioMunicipal de Congresos.

Curiously, one of the drivingforces behind demoscene wasthe limitations of computers

themselves. In the early 1980s, when the movementbegan, the powerful computers we are familiar with todaywere scarcely a pipedream. Only computers with 8bits,such as the Commodore 64, and computers with 64bits,such as the Atari and Spectrum existed. Crackers viedwith each other to break through the videogame copyprotection, and when they were successful they left theirsignatures as a record, even though they only “existed” in

a minute space in the programme. The outcome ofthis story is well known: the signatures of thepirates, demos with original graphics, turned out tobe better than the games themselves. Although theyscarcely occupied any space in the computer, theygenerated animated images that were far bolder andgroundbreaking than those created by the “legal”designers. In fact, many “crackers” have ended upworking for the very companies whose games theypirated. Thus demoscene was born.

Nowadays, such limitations in computer space nolonger materially exist. Though the programmeoccupies very little space, it is still necessary fordefining the technique, and for many of itspractitioners demoscene has lost much of its formerchallenge and forbidden attraction. On the otherhand, it has burgeoned into a form of artisticexpression. Many “demosceners” currently work ingroup networks for which geographical barriershave no importance. “Demoscene parties” are alsoheld, bringing together hundreds of enthusiasts from

Raul Ibáñez, curator of the exhibition

A “bit” of a demoscene composition

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all over the world who create programmes in real timeand compete in different categories.

According to Raúl Ibáñez, curator of the exhibition atthe Centro Cultural Conde Duque, “to achieve the effectswe see in these demoscene works, it is necessary to havea profound knowledge of mathematics and geometry,since it is not possible to use pre-recorded material in thedemonstrations. That’s why all the images must begenerated by mathematical formulae, and all the camerasand lighting are designed and move in real time by meansof complex algorithms”.

A visit to the exhibition “Demoscene: Mathematics inMovement” will enable to general public not only to seethe images created but to talk with the authorsthemselves, who will be explaining their work on themornings of August 24th, 25th and 26th at the CentroCultural Conde Duque, and starting at 18.00 on August24th, 25th and 28th at the Palacio Municipal deCongresos (the main venue of the ICM2005 International

Congress of Mathematicians).

Exhibition: “Demoscene: Mathematics in Movement”(Centro Cultural Conde Duque, 17/8 to 29/10. Entrance

free)http://www.icm2006.org/culturalactivities/other/demosc

ene

More information about activities at the C. C. CondeDuque (including the exhibition on fractal art)www.munimadrid.es/condeduque/

Erratum

In our first Daily News (August 23rd) we added unneeded emphasis to the words of John Ball. During the OpeningCeremony he said: “I regret that Dr Perelman has declined to accept the Fields Medal”. We wrote: “I deeply regret (…)”.

Also, we should clarify that Mario García Fernández wrote only the text about Hamilton plenary lecture that appearedon page 7 of yesterday’s Daily News (August 24th), not the text on page 6. In Mario’s text, where it reads ‘3-manifoldvariety’ it should read only ‘3-manifold’. And where it says ‘variety’it should read ‘manifold’.

The new IMU logo8 ICM 2006 MADRID SPAIN

The new International Mathematical Union (IMU)emblem was presented during the opening ceremony of the2006 International Congress of Mathematicians currentlybeing held in Madrid. The design, by John M. Sullivan,professor of Mathematical Visualization at the BerlinTechnical University (Germany), was chosen by the IMUexecutive committee from among the 80 designs submittedfor consideration since 2004. Sullivan, 42 years old andfrom the USA, works on the study of knot theory anddecided to base his design on images developed for histeam’s article, Criticality for the Gehring Link Problem,soon to appear in Geometry and Topology. The imageshows a Borromean knot, a famous configuration of threeinterlocking rings that fall apart if one of them is removed.This characteristic has for centuries made this type of knot asymbol of unity, co-operation and strength in many cultures,although it is often depicted in the form of three rings orhoops. However, such a structure is mathematicallyimpossible. For that reason Sullivan has given the rings agreater mathematical precision, although he retains in hisdesign their symbolic value to reflect the fundamentalinterrelation between different branches of mathematics.With regard to his motivation, he has this to say:“Personally, I’ve always been drawn to problems where Icould really look at the results visually, as a picture”.

For further information, including video:http://torus.math.uiuc.edu/jms/Images/IMU-logo/

Behind every ICM there’s a hidden background andstory whose details are known to only a few of theprivileged - or should we call them the self-sacrificing, thedevoted, or martyrs to the cause? Whatever the appropriateterm, the list on this occasion (in alphabetical order) is asfollows: Carlos Andradas; Emilio Bujalance; CarlesCasacuberta; Eduardo Casas; Fernando Chamizo;Guillermo Curbera; Antonio Durán; Rosa Echevarría;Marisa Fernández; Pedro Gil; José Luis González Llavona;Raúl Ibáñez; Alberto Ibort; Manuel de León; PabloPedregal; Adolfo Quirós; Miguel Ángel Rodríguez; MartaSanz; Fernando Soria; Juan Luis Varona y Joan Verdera.

The name that ought to figure at the head of this list isManuel de León, chair of the Executive Committee. DeLeón has spent 7 years working towards the day when themathematical community could enjoy one of its bestcongresses to date. It is quite unlikely that when hemoved to Madrid in 1986 to work at the CSIC Institute ofMathematics and Fundamental Physics, de León everimagined that in 20 years time he would be presidingover the committee responsible for organizing the firstICM to be held in Spain.

This 53 year old mathematician from Zamora andGalician by adoption has behind him a solid career that

The spanish face of the Congress:who’s who on the executive committee

László Lovász (Hungary) is the new president of theInternational Mathematical Union (IMU), elected duringthe 25th IMU General Assembly held last week inSantiago de Compostela, Spain. Ma Zhiming (China) andClaudio Procesi (Italy) were elected for the two posts ofvice-president, while the new secretary of theorganization is Martin Grötschel (Germany).

Also during the assembly, approval was given for Indiato host the 26th International Congress of Mathematicians(ICM), which will be held in Hyderabad in 2010. A fewdays prior to this, and in accord with the custom ofholding the General Assembly in a different city of thehost country, the next IMU General Assembly will takeplace in Bangalore. It was also decided to increase the

financial contributions of the wealthiest IMU membercountries to fund mathematical co-operation schemeswith the more disadvantaged nations.

The news at a national level was that Manuel de Leónwas named as a member of the IMU executivecommittee, the first time a Spanish mathematician hasever belonged to this body. Furthermore, another Spanishmathematician, Marta Sanz, was assigned a post with theCommission on Co-operation and Exchange (CDE), oneof the four forming part of the IMU.

The new IMU board

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began in 1975 when he graduated at the University ofSantiago de Compostela. He is the author of more than250 scientific papers and three monographs. He was co-ordinator of the Spanish committee for the InternationalYear of Mathematics in 2000, and is a member of theComisión Asesora de Evaluación y Prospectiva and theRoyal Academy of Exact, Physical and Natural Sciences.

His colleagues describe him as a workaholic, everprepared to embark on new ventures. After meeting thechallenge of organizing this ICM, from January 1st ofnext year he will be the first Spanish member of the IMUExecutive Committee.

As his secretary remarks affectionately: “He has anenormous capacity for work and a great memory. He isorganized and a perfeccionist, but at the same time adaptsto the unexpected with a smile”.

Mathematics in granite

Wielding his hammer in the middle of the street, theJapanese artist Keizo Ushio has since the first day of theCongress been sculpting a geometrical piece that growsand takes on shape from day to day. The work, hewnfrom black granite, consists of two interlacing stripsrepresenting the concept of infinity.

Ushio says he uses mathematics in his works becausethey constitute a universal language that requires notranslation. On this occasion he is working on a piecebased on a torus – a closed surface, the product of theunion of two circumferences – which he willsubsequently split into two halves. This he will do bychiselling out a 360º diameter around the circumferencein the form of a crossed strip. Ushio will then rejoin thetwo parts to create a new shape which, depending on theangle it is viewed from, will evoke the mathematicalsymbol for infinity. The sculptor estimates that the workwill be completed by August 30th, and after theconference this mathematical sculpture will be transferredto the CSIC (Consejo Superior de InvestigacionesCientíficas) building.

Mathematics can also be used forpeace

ROUND TABLE: FRIDA Y, AUGUST 25TH: 19.00,ROOM L101

The “Mathematics for Peace” summer school, held inCórdoba in July and running in parallel with the ICMscientific programme, took place in a social context thatthe ICM is keen to strengthen. On this occasion it was thegeopolitical situation of Spain as a meeting point of threeaxes: the European axis, the Mediterranean Axis, and theLatin American axis. 150 students and teachers of morethan twenty different nationalities participated in theschool, which they were able to enjoy thanks to thealtruistic co-operation of prestigious universities andinstitutions from different parts of the world. The schoolwas the first of many events organized around this themefor the Congress, such as the round-table discussion“Mathematics for Peace and Development”, which willtake place today at 7.00pm in Room L101. All theparticipants have first-hand experience in projects of co-operation and support for the development ofmathematics in a social context.

Mary Gray, the first chair and one of the founders ofthe Association for Women in Mathematics, will guidethe discussion. Applied statistics and the subjects oflanguage and gender in mathematics are among heracademic pursuits. In 1993, she occupied the post ofchairperson for the USAbranch of Amnesty International.

Also taking part in the round table are: Manuel de León(member of the CSIC Commission for Science and PhysicsTechnology) whose career has focused on differentialgeometry and geometric mechanics; Roberto Markarian,expert in Ergodic Theory and founder of the UMALCA(Unión Matemática de América Latina y el Caribe).

Other participants in the round table will be: MarwanAwartani of Birzeit University, who has often acted asconsultant to international institutions such as UNESCO,the European Union, the UNDPand the USAID; andMohammad Saleh, also of Birzeit University. They willbe joined by Mina Teicher, of the Israelian Ministry ofScience and Technology and director of the EmmyNoether Institute of Mathematical Research. Representingthe Spanish Ministry of Foreign Affairs will be AlbertoMiranda, Technical Consultant to the Ibero-AmericanCooperation Board.

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En estos días decir Nevanlinna es casi un sinónimodel nombre del matemático estadounidense JonKleinberg (Universidad de Cornell, EEUU) premiadocon este galardón que reconoce, cada cuatro años,los avances realizados en el binomio matemáticas ySociedad de la Información. Por eso, su conversa-ción deriva rápidamente a temas como comercioelectrónico; nuevos tipos de economía on line;mundo interconectado o la calidad de la informaciónque se encuentra en la Red, un punto vital en unasociedad cada vez más informatizada. Kleinbergreflexiona sobre todos estos aspectos con las mate-máticas como trasfondo, dado que son la herramien-ta que le sirve para crear modelos basados en teoríade la probabilidad; son modelos que utiliza, en ciertomodo, para entender el comportamiento humano. "Aveces pensamos que los ordenadores piensan;mientras que sólo procesan datos. Por eso es intere-sante que analicemos la manera en que los usamos,porque al final ellos sólo son intermediarios entre lagente. Al entender cómo trabajamos con ellos, obte-nemos datos muy valiosos. Porque los textos, porejemplo, son como la gente. Y si aplicamos la proba-bilidad a esos documentos, encontramos modelosmatemáticos que nos revelan datos interesantes,información con un valor económico que habla decomportamiento humano, de usos, gustos, formas depensar", explica.

Para él una de las claves es cómo organizamos lainformación y cómo la estructuramos. Y de ahí a unabúsqueda estructurada y eficaz hay un paso, que esdonde el matemático aplica la probabilidad. Su obje-tivo: hacer que la experiencia en la Web sea más efi-caz. Kleinberg ha desarrollado un modelo matemáti-co para que las búsquedas de información en la Redo en una bandeja de correos electrónicos sean másinteligentes. Se trata, según explica, de entender queuna búsqueda en Internet se puede hacer de dos for-mas: tipo biblioteca (en la que el usuario pide a lamáquina todo el material que haya respecto a unamateria); y de otra manera más inteligente, quedetecta cuándo un evento ha sido noticia y, por tanto,de interés. Para hacer factible esta segunda búsque-da, Kleinberg detecta en los textos las palabras quemás se repiten y luego valora las que sirven de clavepara que la máquina indique que ocurre algo, queese texto o documento tiene algo anómalo. "Es unmodelo matemático que da un valor a cada palabradependiendo de su interés", explica. Es decir, al ana-

lizar por ejemplo 200 años de los discursos de lospresidentes estadounidenses, Kleinberg da con queciertas palabras le marcan acontecimientos especia-les, noticias. Para verlo, pongamos el ejemplo en ungráfico. En el eje de las ordenadas pondríamos elnúmero de veces que aparece una palabra concreta:Vietnam, por ejemplo. En el de las abscisas iría unatabla de tiempo (1800, 1850, 1900, 2000). Pues bien,la tabla mostraría rápidamente que sobre 1950 ocu-rrió algo muy importante relacionado con la políticaestadounidense y Vietnam. Si la palabra patrón o ele-gida hubiera sido el artículo "el", la línea sería cons-tante; no haría picos, no indicaría nada reseñable.Esa forma de escanear los textos también valdríapara saber, por ejemplo, que el 11 de Marzo de 2004en Madrid ocurrió algo fuera de lo normal en la capi-tal de España. Imagínese el lector que quiere, en unmotor de búsqueda de noticias, información sobreMadrid. El buscador tipo biblioteca ofrecería todaslas referencias sobre la ciudad (museos, monumen-tos, historia de la ciudad, noticias…); en cambio, enesa búsqueda de noticias selecta, veríamos que derepente Madrid, el día 11, sube repentinamente, indi-cando que algo pasó y además de forma imprevisi-ble. Esto último se refleja en que el cómputo de refe-rencias subiría de 0 a x en vertical -sin una curvaascendente, un pico y otra descendente, algo propiode un evento ya anunciado, como unas elecciones-.Y esa misma técnica se aplica al correo electrónico."Mi correo es muy aburrido y todo es de trabajo. Perogracias a este método puedo seleccionar o buscar loque me interese y saber en qué he estado trabajan-do", explica. Y preguntado por cuáles serían las pala-bras clave para entender su pensamiento, las quemás aparecen en su email, Kleinberg dice que sucorreo es todo trabajo, aunque apunta una aplicaciónpráctica: "He podido buscar nombres propios de ami-gos de hace seis años, gente con la que ya no teníacontacto y que pidiéndole a la máquina patrones debúsqueda ha sabido decirme que teníamos una rela-ción hace años: aparecían esos picos como informa-ción frecuente", explica el matemático.

Sobre si tendremos pronto un buscador que piensecomo una persona, el reciente premio Nevanlinnadice que no. "No hay nada tan enriquecedor comohablar directamente con un experto para entenderalgo; todavía no hay una forma de leer, ver o asimilarconocimiento más enriquecedora que el contactodirecto de una persona, sin máquinas de por medio",apunta.

Y Kleinberg vuelve a cómo la sociedad ha cambia-do en los últimos 15 años por la popularización delPC. "Los ordenadores están creando un nuevo

Daily News (Versión en Español)

JON KLEINBERG: “LOS TEX-TOS SON COMO LAGENTE”

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mundo, y en ese espacio virtual las reglas son muchomás flexibles. En física las reglas son de oro, pero noaquí. La Web representa una nueva forma de pen-sar", señala. En ese ámbito la información, y por lotanto su organización, es cada vez más importante.Pero no hay normas. Y por ejemplo, su método novaldría para discernir sobre la calidad de la informa-ción de un blog. "Ahora [que todo el mundo puedepublicar] la información válida es la que tiene la repu-tación. ¿Y cómo sabemos si una fuente tiene reputa-ción?", se pregunta el propio Kleinberg. La respuestaestá, añade, en el grado de precisión, algo que nosaben valorar los ordenadores. "Lo sabemos nos-otros, que sabemos qué periódicos están bienhechos, y quién los elabora y contrasta la informa-ción". Porque sí, un blog puede tener hasta 200 lec-tores por día, pero eso no significa que la informaciónallí vertida sea veraz: "Por eso se puede predecir queun periódico tendrá información precisa: de ellodepende su reputación", concluye.

ASPECTOS DESTACADOS DEL TRABAJO DEJON KLEINBERG

El trabajo de Jon Kleinberg ha proporcionado unavisión teórica para abordar importantes cuestionesprácticas que se han convertido en esenciales parala comprensión y la gestión de nuestro cada vez másinterconectado mundo. Ha trabajado en una ampliavariedad de áreas, desde el análisis de redes y elenrutado, a la minería de datos, la genómica compa-rativa o el análisis de la estructura de las proteínas.Además de haber realizado contribuciones funda-mentales en investigación, Kleinberg ha reflexionadosobre el impacto de la tecnología es sus esferassocial, económica y política.

Uno de los más importantes logros de Kleinberg secentra en la estructura de red de la World Wide Web.Sus aportaciones han tenido una enorme influenciaen la forma de operar de los más importantes siste-mas de búsqueda en internet. Mientras que las pági-nas web individuales tienen un grado de estructuraimpuesto por sus creadores, la estructura de laWWW en su conjunto carece por completo de plani-ficación; emerge y cambia continuamente a medidaque se incorporan nuevos enlaces y contenidos. Porello, es todo un desafío el diseño de formas eficien-tes de seleccionar las páginas relevantes para ofre-cer a los usuarios de los sistemas de búsqueda.Antes del trabajo de Kleinberg, estos sistemas secentraban solo en el contenido de las páginas, no enla estructura de enlaces. En 1996, Kleinberg introdu-jo las ideas de “autoridades” y “hubs”. La primera serefiere a las páginas que contienen informaciónsobre un tema concreto, y la segunda a las que tie-nen enlaces a muchas “autoridades”. Por ejemplo, sise teclea la búsqueda de “cámaras digitales”, unaweb que ofrezca guías, comentarios o un panoramageneral sobre diferentes cámaras será un “hub”,

mientras que las páginas de los fabricantes serán“autoridades”. Aunque la distinción entre ambos con-ceptos es intuitivamente sencilla, definirlos matemá-ticamente es difícil por la circularidad que presenta:un “hub” ofrece conexiones a muchas “autoridades” ycada una de éstas tiene enlaces con muchos “hubs”.La contribución clave de Kleinberg fue proporcionaruna forma para romper esta circularidad, abriendo elcamino para un análisis matemático de la estructurade enlaces de las redes. Kleinberg desarrolló lasherramientas algorítmicas para resolver este proble-ma y demostró su efectividad probándolas en laWorld Wide Web.

Otro campo en el que Kleinberg ha realizado apor-taciones fundamentales es en las redes del tipo “elmundo es un pañuelo”. Estas redes fueron ideadaspor el psicólogo Stanley Milgram en experimentosrealizados en los años 60, y se convirtieron en elcentro de diferentes modelos matemáticos basadosen el trabajo de Duncan Watts y Steve Strogatz enlos 90. En los experimentos de Milgram, “A” debíahacer llegar un mensaje a “B”, a quien no conocíadirectamente, a través de otras personas, en elmenor número de pasos posible. Cada persona dela cadena solo podía enviar el mensaje a otra queconociera personalmente. Milgram observó que, demedia, el mensaje llegaba a su destinatario en tansolo seis pasos (éste es el origen de la expresión“seis grados de separación”). El número 6 es sor-prendentemente pequeño, dado el tamaño de lapoblación global y que cada persona operaba solocon información local de la red. Hasta bien avanza-dos los 90, había una amplia literatura científicasobre la existencia de atajos para conectar indivi-duos en la red social, pero apenas se había presta-do atención a la forma de encontrar estos caminossolo con información local: ¿cómo puede encontrarel camino más corto gente que no tiene una visiónglobal de la red completa y solo conoce a sus ami-gos inmediatos? Esta es la pregunta que Kleinbergse hizo, y descubrió algunas cosas sorprendentes.

Los nodos de una red social son las personas quela forman. Dos nodos están conectados si las dospersonas se conocen mutuamente. Kleinbergobservó que en una red de este tipo la probabilidadde que dos nodos se conecten desciende a medidaque aumenta la distancia geográfica entre ellos, ymostró que si lo hacía con el cuadrado de ladistancia entre ellos, existían algoritmos capaces deencontrar el camino más corto entre ambos. Deforma más sorprendente aún, mostró que sidecrecía más rápido o más despacio que elcuadrado de la distancia no existía ese algoritmo.Además de resolver aspectos teóricos de redes deeste tipo, el trabajo de Kleinberg ha sido útil en eldesarrollo de sistemas P2P de intercambio dearchivos, en los que la información tiene quelocalizarse sin que esté centralizada.

Uno de los primeros resultados de Kleinbergtambién se refiere a algoritmos eficientes, en esta

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ocasión para el problema de encontrar “vecinoscercanos” en grupos de datos de alta dimensión. Elproblema se presenta en situaciones como lassiguientes. Supongamos que tenemos un grupo dedocumentos y un diccionario de n palabras. Paracada documento contamos el número de veces queaparece la primera palabra del diccionario, lasegunda, la tercera, etc. De esta forma, obtenemosn cuentas, que pueden ser consideradas como unvector de n dimensiones representativo deldocumento. Para un documento cualquiera, “A”,¿cómo podemos identificar el vecino más próximo,es decir, el documento “B” que es el más parecido aA de todos los documentos del grupo? Pensando enestos documentos como vectores, lo quepretendemos es encontrar B de forma que ladistancia entre A y B sea lo más pequeña posible.Una solución, por supuesto, consiste simplementeen medir las distancias entre A y todos los demásvectores y mirar cual es la más corta. Pero si n (elnúmero de palabras en el diccionario) es muygrande, nos enfrentamos con un espacio de muyaltas dimensiones, donde esta técnica de fuerzabruta, de comprobar todas las posibilidades seconvierte rápidamente en una “carrera dedimensionalidad” y en consecuencia, cara yexcesivamente larga. Kleinberg rompió la situaciónde estancamiento desarrollando una nueva eingeniosa aproximación al problema del vecino máscercano, mediante la combinación aleatoria deproyecciones unidimensionales de los vectores.

Otro hito en el trabajo de Kleinberg es el desarro-llo de un modelo matemático para reconocer fogona-zos en el interior de flujos de datos. Una forma deanalizar la estructura de la información contenida enun texto es localizar las explosiones de actividadque aparecen repentinamente y se sostienen duran-te un cierto periodo de tiempo. Por ejemplo, aunqueusted no hable inglés, si observa la aparición repen-tina de la palabra “Katrina” y la elevada frecuenciade su uso en los medios de comunicación en agos-to de 2005, usted comprenderá que algo significati-vo ha ocurrido. Kleinberg empezó estudiando estosfogonazos por una razón eminentemente práctica:quería encontrar el mejor medio para organizar supropio archivo personal de mensajes electrónicosque se le estaban acumulando. Aunque la idea deestos fogonazos de actividad informativa es intuitiva-mente clara, definir con rigor la noción no es senci-llo, debido a la dificultad de distinguir estos fenóme-nos de las fluctuaciones estadísticas en un mar deinformación aleatoria. La aportación fundamental deKleinberg fue proporcionar semejante definición, uti-lizando el concepto matemático de los modelos deMarkov. Comprobó sus ideas con diferentes gruposde datos, como los títulos de los artículos científicosdistribuidos muchas décadas antes en un áreadeterminada. En este caso, los fogonazos corres-pondían a la aparición y atención prestada a nuevos

temas en ese área de investigación.La interacción entre la comprensión teórica de las

redes y la observación de redes en funcionamientoha impregnado la investigación de Kleinberg y pro-porcionado nuevas perspectivas sobre el papel de latecnología en la sociedad. “Internet y la web nosobligan a pensar sobre las consecuencias socialesde un mundo en el cual la información es más com-pleta y viaja más ampliamente que nunca antes, y enel que cualquiera tiene la posibilidad, a través denuevos mecanismos de comunicación y a un preciomuy bajo, de convertirse en un autor con unaaudiencia global”, escribió Kleinberg en una entre-vista por correo electrónico con la revista digitalNoticias de Investigación Tecnológica (TechnologyResearch News). “Pero hay un buen número deretos aquí. Sabemos que el discurso on-line puedeestar altamente polarizado, ¿significa que las herra-mientas on-line que hemos creado están contribu-yendo a incrementar el nivel de polarización en eldiálogo social en general? ¿Cómo podemos deter-minar con certeza este fenómeno y qué debemospensar sobre el diseño de nuevos instrumentos parahacer el discurso on-line más productivo?” El traba-jo de Kleinberg se distingue por su riqueza y diversi-dad, y también por su habilidad para utilizar visionesteóricas y profunda comprensión en su aplicación aproblemas prácticos. Esta poderosa combinaciónasegura a Kleinberg un papel estelar como uno delos pensadores más influyentes en la ciencia decomputación teórica de los próximos años.

DEMOSCENE: DELPIRATEOINFORMÁTICO AL ARTE

Empezó como un hobby, una competición entreprogramadores para ‘crackear’ videojuegos, una sub-cultura urbana. Y se ha convertido en una forma deconferir alma artística al amasijo de microchips conque trabajamos cotidianamente. El ‘demoscene’ esuna forma de arte con ordenadores que consiste encrear imágenes animadas, generalmente con músi-ca, con programas que corren en tiempo real. Sudesarrollo demuestra un conocimiento profundo dematemáticas y geometría. Para ver, entender e inclu-so participar en una muestra de demoscene, nadamejor que visitar la exposición montada en el CentroCultural Conde Duque, en Madrid, del 17 de agostoal 29 de octubre. Es una de las actividades culturalesparalelas al Congreso Internacional de MatemáticosICM2006, y está teniendo tanto éxito que el comisa-rio de la muestra, Raúl Ibáñez, no pudo evitar ayercomentar: “Es la primera vez que veo cola en unaexposición sobre matemáticas”. Ayer por la tardetuvo lugar en el Palacio Municipal de Congresos unamuestra de realización de demoscene en directo.

Curiosamente, parte del motor del demoscene fue-ron las limitaciones de los ordenadores. A principios

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de los ochenta, cuando empezó el movimiento, lospotentes ordenadores actuales ni se soñaban.Estaban las computadoras de 8bits, como elCommodore 64, y de 64bits, como el Atari o elSpectrum. Los crackers competían en quitar las pro-tecciones anti-copia de los juegos y, al hacerlo, deja-ban su firma; una firma digna de ser recordada, aun-que debía ‘existir’ en un espacio minúsculo de pro-grama. El final es previsible. Las firmas de los piratasacabaron siendo mejores que el propio juego: pese ano ocupar apenas espacio en la computadora, gene-raban animaciones mucho más atrevidas y rompedo-ras que las creadas por los diseñadores ‘legales’ –yde hecho muchos ‘crackers’ han acabado trabajandopara las compañías cuyos juegos pirateaban—.Había nacido el demoscene.

Hoy en día las limitaciones de espacio en las com-putadoras ya no existen materialmente –aunque queel programa ocupe poco espacio sigue siendo unrequisito que define la técnica—, y el demoscene haperdido, para la mayoría de sus ‘practicantes’, granparte de su viejo espíritu guerrero. Pero, a cambio,ha estallado como forma de expresión artística.Actualmente es habitual que los ‘demosceners’ tra-bajen en grupo y en red, sin importar las barrerasgeográficas. También se celebran ‘fiestas demosce-ne’, en las que se dan cita centenares de aficionadosen todo el mundo para crear sus programas en tiem-po real y competir en diversas categorías.

Como explica Raúl Ibáñez, comisario de la exposi-ción en el Centro Cultural Conde Duque, “para con-seguir los efectos que se muestran en las obras dedemoscene es necesario tener un conocimiento muyprofundo de matemáticas y geometría, porque no esposible usar en las demostraciones material grabadopreviamente. Por eso todas las imágenes deben sergeneradas por fórmulas matemáticas, y todas lasluces y cámaras se diseñan y mueven en tiempo realmediante complejos algoritmos”. En la exposición“Demoscene: matemáticas en movimiento” el públicopodrá, además de contemplar las obras, hablar conlos autores. Estos llevan explicando sus obras desdelos días 24, 25 y 26 de agosto por la mañana en elCentro Cultural Conde Duque, y los 24, 25 y 28 a las18:00 en el Palacio Municipal de Congresos (sededel Congreso Internacional de MatemáticosICM2006).

NUEVA DIRECTIVA DE LA IMU

László Lovász (Hungría) es el nuevo presidentede la Unión Matemática (UMI), elegido en la XVAsamblea General de la Unión MatemáticaInternacional celebrada el pasado fin de semanaen Santiago de Compostela, España. Las vicepre-sidencias recayeron en Zhi-Ming Ma (China) yClaudio Procesi (Italia) y la secretaría de la organi-zación en Martin Grötschel (Alemania).

Durante la asamblea también se aprobó que India

sea la sede del próximo Congreso Mundial deMatemáticos (ICM), el XXVI, que se celebrará en laciudad de Hyderabad, en el año 2010. Días antes, ysiguiendo la tradición de que la Asamblea tenga lugaren el mismo país, pero en una ciudad diferente a laelegida para el Congreso, se celebrará la próximaAsamblea General de la IMU en Bangalore.

Se decidió también incrementar el presupuesto delos países más ricos para financiar las actividades decooperación matemática que se realizan en los másdesfavorecidos.

Dentro del ámbito nacional, cabe destacar el nom-bramiento del español Manuel de Léon como miem-bro de la ejecutiva de la IMU. Es la primera vez queun español ingresa en dicho grupo. Además, otramatemática española, Marta Sanz, ha conseguido unpuesto en la Comisión de Cooperación y Desarrollo(CDE), una de las cuatro que mantiene la Unión.

LA IMU ESTRENALOGO

El nuevo emblema fue presentado durante la cere-monia de inauguración del Congreso Internacionalde Matemáticos 2006, que se está celebrando estosdías en Madrid. El diseño de John M. Sullivan, profe-sor de Visualización Matemática en la UniversidadTécnica de Berlín (Alemania) fue elegido por elComité Ejecutivo de la IMU entre un total de 80 pro-puestas presentadas a un concurso convocado en2004. Sullivan, estadounidense de 42 años, que sededica al estudio de la teoría de nudos, decidió tra-bajar sobre imágenes desarrolladas para el artículode su equipo, Criticality for the Gehring Link Problem,que aparecerá próximamente en Geometry andTopology. La imagen muestra un nudo borromeo, unafamosa configuración de tres elementos enlazadoscon la particularidad de que, si se retira uno de ellos,los otros dos se desligan. Esta característica lo haconvertido durante siglos en símbolo de unión, inter-acción y fuerza en muchas culturas, si bien se suelerepresentar formado por tres círculos redondos. Sinembargo, esa estructura es matemáticamente impo-sible. Por ello, Sullivan los ha dotado de mayor preci-sión matemática, aunque ha recogido su valor simbó-lico para reflejar fundamentalmente la interrelaciónentre los distintos ámbitos matemáticos. Respecto asu motivación, asegura: “personalmente siempre mehan atraído los problemas cuya solución podía con-templar visualmente, como una imagen”.

Más información, incluido un vídeo:http://torus.math.uiuc.edu/jms/Images/IMU-logo/

14 ICM 2006 MADRID SPAIN

La cara española del congresoQUIÉN ES QUIÉN EN ELCOMITÉ EJECUTIVO

Detrás de cada ICM hay oculta una historia que sólopueden contar unos pocos privilegiados. O más bienabnegados. O más bien devotos… ¿Mártires de lacausa? Queda a cada cual la elección del términocorrecto. Ellos son (por orden alfabético): CarlosAndradas; Emilio Bujalance; Carles Casacuberta;Eduardo Casas; Fernando Chamizo; GuillermoCurbera; Antonio Durán; Rosa Echevarría; MarisaFernández; Pedro Gil; José Luis González Llavona;Raúl Ibáñez; Alberto Ibort; Manuel de León; PabloPedregal; Adolfo Quirós; Miguel Ángel Rodríguez;Marta Sanz, Fernando Soria, Juan Luis Varona yJoan Verdera.A la cabeza de todos ellos, Manuel de León, presi-dente del Comité Ejecutivo. De León lleva más de 7años trabajando para que estos días la comunidadmatemática disfrute de uno de sus mejores congre-sos. Seguro que cuando en 1986 se mudó a Madridpara trabajar en el Instituto de Matemáticas y FísicaFundamental del CSIC no se imaginaba que, al cabode 20 años, presidiría el comité encargado de orga-nizar el primer ICM que tiene lugar en España.Este matemático zamorano, y gallego de adopcióntiene tras de sí, a sus 53 años, una trayectoria sóli-da que comenzó cuando se licenció en laUniversidad de Santiago de Compostela en 1975. Esautor de más de 250 trabajos científicos y de treslibros monográficos; fue coordinador del comitéespañol del Año Internacional de las Matemáticascelebrado en 2000; es miembro de la ComisiónAsesora de Evaluación y Prospectiva; y académicode la Real Academia de Ciencia Exactas, Físicas yNaturales. Quienes trabajan con él dicen que es un adicto altrabajo –lo que explica que se embarque en estasaventuras-. Después de superar el reto de organizarel actual congreso, a partir del 1 de enero será el pri-mer español miembro de la ejecutiva de la UniónMatemática Internacional.“Es un trabajador al máximo, con una gran memoria,organizado y perfeccionista, pero que se adapta atodos los imprevistos y situaciones con una sonrisa”,dice cariñosamente su secretaria.

MATEMÁTICAS CON FORMA DE GRANITO

El artista japonés Keizo Ushio, a martillazo limpio yen plena calle, esculpe desde el primer día del con-greso una enorme escultura geométrica que “crece”y toma forma día a día. La obra, construida en grani-to negro, consiste en dos bandas entrelazadas querepresentan el concepto de infinito. Para ver cómotoma forma sólo hay que pasear junto a la entradaprincipal del recinto ferial.

El autor utiliza las matemáticas en sus trabajos por-que dice que representan un lenguaje universal queno necesita traducción. En esta ocasión el artista rea-lizará una pieza basándose en la figura del Toro -unasuperficie cerrada, producto de la unión de dos cir-cunferencias- que dividirá en dos partes. Para ello,cincelará un diámetro de un ángulo de 360 gradosalrededor de la circunferencia con la forma de unacinta cruzada. Con esa base, Ushio combinará losdos fragmentos resultantes, creando así una nuevaforma que, según desde el ángulo que se miré, podráevocar el signo matemático de infinito. El escultorestima que terminará la escultura el próximo día 30.Una vez finalice el Congreso, la escultura matemáti-ca será trasladada al CSIC (Consejo Superior deInvestigaciones Científicas).

LAS MATEMÁTICAS TAMBIÉNSIRVEN PARA LA PAZ

Mesa redonda, Viernes 25 de Agosto,19:00 h, sala L101

La escuela “Matemáticas por la paz” tuvo lugar enCórdoba el pasado julio, teniendo como contexto eltema de contenido social, paralelo al programa científi-co, que se intenta fomentar durante los ICM –y que enesta ocasión ha sido la situación geopolítica de Españacomo punto de encuentro de tres ejes: el europeo, elmediterráneo y el latinoamericano—. En la escuelaparticiparon 150 alumnos y profesores de más de vein-te nacionalidades, que pudieron disfrutarla gracias a lacolaboración de manera altruista de prestigiosas uni-versidades e institutos de todo el mundo. La escuela hasido sólo un antecedente de las actividades que sesiguen desarrollando durante el Congreso con respec-to a este tema, como la mesa redonda “Matemáticaspara la paz y el desarrollo” que se celebra hoy a las 19horas en la sala L101. Todos los ponentes que colabo-ran en ella tienen en su trayectoria proyectos de cola-boración y ayuda al desarrollo de las matemáticas den-tro del contexto social.

Como moderadora, Mary Gray, primera presidentade la Asociación para las Mujeres en Matemáticas.También participarán en la mesa Manuel de León(miembro de la Comisión del Área de Ciencias y tec-nologías Físicas del CSIC), cuyo trabajo científico secentra en la geometría diferencial y mecánica geo-métrica; Roberto Markarian, fundador de la UniónMatemática de América Latina y el Caribe. Otroscomponentes de la mesa redonda son: MarwanAwartani, de la Birzeit University, que ha ejercido endiversas ocasiones como consultor de institucionesinternacionales como la UNESCO, la UE, UNDP yUSAID; y Mohammad Saleh, también de la BirzeitUniversity. Junto a ellos estará Mina Teicher, delMinisterio de ciencia y Tecnología de Israel. Por partedel ministerio español de Asuntos Exteriores estaráAlberto Miranda, Consejero Técnico de la DirecciónGeneral de Cooperación con Iberoamérica.

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FRI 25, 19:40-20:00 SC 18 R204Marius Radulescu,Institute of Mathematical Statistics and

Applied Mathematics, Bucharest, RomaniaOn the efficient frontier associated to portfolio selectionmodelsChair: Wenceslao González

SHORT COMMUNICA TIONS (cancelled)FRI 24, 17:35-17:55 SC 02 R402 Vijay Kumar Bhat

SHORT COMMUNICA TIONS (changes respect to theprinted pr ogram)

FRI 24, 14:55-15:55 SC 07 Elizabeth Mann. New date:MON 28, 17:35-17:55Fri 25, 18:00.

The RSME will award the prize José Luis Rubio deFrancia for young researchers to Javier Parcet. Prize willbe awarede at the beginning of the Joint Activity LSM-RSME in room L-202.

Moving (Mostly) Forward Women in Mathematics,August 25. 18:00-20:00 (free access)

LSM-RSME Special Lectures, August 25, 18:00-20:00Special Lecture B. Mandelbrot. The nature of

roughness in mathematics, science and art (free access)

FRI 25, 14:00-14:45 ILALecture by the Rolf Nevanlinna Prize WinnerJon Kleinberg, Cornell University, Ithaca, USAThe structure of information networksChair: Gert-Martin Greuel

FRI 25, 19:00-20:30, L101Round TableMathematics for Peace and DevelopmentModerator: Mary W. Gray, American University, USAPanelists:Marwan Awartani, Secretary General of the

Universal Education Foundation, Birzeit University,Palestine

Mohammad Saleh, Palestinian Society forMathematical Sciences

Manuel de León, CSIC, ICM2006 MadridRoberto Markarian, Universidad de la República,

Uruguay, Unión Matemáticas de América Latina y elCaribe (UMALCA)

Mina Teicher, Bar-Ilan University, Israel

NEW ACTIVITIES:Friday, August 25, 19:00-20:00, Room L103Presentation of The Mundus Master ALGANT, an

integrated study programme, founded on the collaborationof four European universities, open to all studentsinterested in a strong preparation towards research inalgebra, geometry and number theory.

Speakers: Boas EREZ (Université Bordeaux 1),Philippe CASSOU-NOGUÈS (Université Bordeaux 1),Henri DARMON (Mc Gill University).

Summary: We present a two-year study track built uponthe master programmes in mathematics of the universitiesin Bordeaux (France), Leiden (The Netherlands), Padova(Italy) and Paris (France). Recently the collaboration hasbeen extended to the universities in Montreal (Canada).

The track, chiristened ALGANT for Algebra, GeometryAnd Number Theory, takes students through at least twoof the European partner universities in different countries,and the integrated study programme leads to a multiplenational degree. The track thus defined has been selectedas one of the Erasmus Mundus Masters by the EuropeanCommission in 2004. It is the only one in puremathematics. This recognition allows the consortium tooffer every year some 25 two-year scholarships tostudents from countries not in the European Union. Eachscholarship amounts to 21000 € a year. We can also offerscholarships to European students, whom we also offerthe opportunity to benefit from a studying period inMontreal.

More information in http://www.math.u-bordeaux.fr/ALGANT/

INFORMAL SEMINARS 25TH AUGUST13:00 – 14:00 “Meeting of the African

Mathematician” , Room L203

Prof. Abderrahman Boukricho, President of the AfricanMathematical Union

SUMMARY: in every ICM, the African MathematicalUnion invite all African Mathematicians to an informalmeeting and to discuss about next activities inmathematics. .

16:00 – 16:40 “Infinitesimal deformations and rigidityat non-symmetric affine connections space” , Room L205

Ljubica Velimirovic, ljubicavelimirovic@yahoo.com,Faculty of Science and mathematics, University of Nis,

Serbia

SUMMARY: We consider infitesimal deformations f:xi à xi of a space LN of non-symmetric affine connection.We use four kinds of covariant derivative to express theLie derivative and consider the rigidity of somegeometric objects.

17:00 – 17:40 “Exact controllability of the Nonlinearthird-order Dispersion Equation – An approach ofmonotone operators and Integral contractors” , RoomL205

Dr. Dimplekumar N. Chalishajav,dipu17370@yahoo.com,

SVIT, Vasad, India

I C M 2 0 0 6Daily News

Madrid, August 25th 2006

INVITED LECTURES (cancelled)FRI 25, 18:00 – 18:45 IL12 R401Hubert Saleur, Centre d’Études Nucléaires de Saclay, Gif-

sur-Yvette, France. Wess Zumino field theories onsupergroups

Chair: Jean-Michel Maillet

SHORT COMMUNICA TIONS (new)FRI 25, 17:15-17:35, SC 8 R405Manav Das, University of Louisville, Kentucky, USA

WSP, finite type and OSCChair: Abul Hasan Siddiqi

FRI 25, 17:35-17:55. SC 16 R103Pavel Koryakin, Institute for Mathematical Modeling

Russian Academy of Science, Moscow, Russian Federation,The singularity diagnostics in numerical solving systems ofODEChair: Luis M. Abia

FRI 25, 18:30-18:55 SC 20 L402Ari Belenkiy, Bar-Ilan University, Ramat Gan, Israel

Newton and regression analysisChair: Livia Giacardi

FRI 25, 18:50-19:10 SC 18 R204Jorge Zubelli, IMPA, Rio de Janeiro, Brazil. Asymptotics

of fast mean-reversion stochastic volatility modelsChair: Wenceslao González

FRI 25, 19:20-19:40 SC 18 R204LMMS Ferreira, Universidade do Porto, Portugal

Prisoner’s dilemma in an Edgeworthian economyChair: Wenceslao González

FRI 25, 19:20-19:40 SC 14 R101Sandro Rajola, Università di Roma La Sapienza, Roma,

Italy, Hamiltonian graphs

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PROGRAME CHANGES ANDNOTES OF INTEREST

WARNING! DON’T BE FOOLED BY THE FALSE POLICEMAN TRICK!Unfor tunately, some twenty congress participants were the victims of theft yesterday right outside the main

entrance to the building. All the cases coincide; thieves disguised in blue police uniforms, sometimes in cars andsometimes on foot, ask people foridentification, r emove money from wallets and make off with it. The congressorganizers have contacted the police authorities. All par ticipants are strongly advised to be careful, if asked topresent theirdocuments.

Keizo at work!!Read about himon page 9.