Upload
others
View
4
Download
0
Embed Size (px)
Citation preview
A M E R I C A N M A T H E M A T I C A L S O C I E T Y
PROVIDENCE, RHODE ISLAND USA ISSN 0273-0979 (print) ISSN 1088-9485 (online)
of the( N E W S E R I E S )
BULLETIN
Articles Susan Friedlander Chief Editor
Book Reviews Peter Kuchment
Editors
VOLUME 53 NUMBER 4 OCTOBER 2016
Available electronically at www.ams.org/bull/
Bulletin (New Series) of the American Mathematical Society
The Bulletin publishes expository articles on contemporary mathematical research writ-ten in a way that gives insight to mathematicians who may not be experts in the particulartopic. The Bulletin publishes, by invitation only, reviews of selected books in mathematicsand short articles in the “Mathematical Perspectives” section.
The book review appearing on pp. 701–705 of this volume is reprinted with permission.Copyright c©2015 Society for Industrial and Applied Mathematics. All rights reserved.
Submission information. See Information for Authors at the end of this issue.Publication on the AMS website. Articles are published on the AMS website
individually after proof is returned from authors and before appearing in an issue.Subscription information. Bulletin (New Series) of the American Mathematical
Society is published quarterly. It is available electronically from www.ams.org/journals/.
For paper delivery, subscription prices for Volume 53 (2016) are US$574 list, US$459.20institutional member, US$344.40 individual member, US$516.60 corporate member. Thesubscription price for members is included in the annual dues. Subscription renewalsare subject to late fees. See www.ams.org/journal-faq for more journal subscriptioninformation. If ordering the paper version, add US$5 for delivery within the UnitedStates; US$8 for delivery outside the United States.
Back number information. For back issues see www.ams.org/backvols.Subscriptions and orders should be addressed to the American Mathematical Society,
P.O. Box 845904, Boston, MA 02284-5904 USA. All orders must be accompanied by pay-ment. Other correspondence should be addressed to the American Mathematical Society,201 Charles Street, Providence, RI 02904-2294 USA.
Copying and reprinting. Individual readers of this publication, and nonprofit li-braries acting for them, are permitted to make fair use of the material, such as to copyan article for use in teaching or research. Permission is granted to quote brief passagesfrom this publication in reviews, provided the customary acknowledgment of the sourceis given. Republication, systematic copying, or multiple reproduction of any material inthis publication is permitted only under license from the American Mathematical Soci-ety. Permissions to reuse portions of AMS publication content are now being handledby Copyright Clearance Center’s RightsLink�service. For more information, please visithttp : //www.ams.org/rightslink.
Translation rights and licensed reprint requests should be sent to [email protected].
Excluded from these provisions is material for which the author holds copyright. Insuch cases, requests for permission to reuse or reprint should be addressed directly to theauthor(s). Copyright ownership is indicated in the notice in the lower right-hand cornerof the first page of each article.
Bulletin (New Series) of the American Mathematical Society (ISSN 0273-0979 (print); ISSN 1088-9485 (online)) is published quarterly by the American Mathematical Society at 201 Charles Street,Providence, RI 02904-2294 USA. Periodicals postage is paid at Providence, Rhode Island, and addi-tional mailing offices. POSTMASTER: Send address changes to Bulletin (New Series) of the AmericanMathematical Society, American Mathematical Society, 201 Charles Street, Providence, RI 02904-2294USA.
c© 2016 American Mathematical Society. All rights reserved.
This journal is indexed in Mathematical Reviews, Science Citation Index�,Science Citation IndexTM–Expanded, ISI Alerting ServicesSM, CompuMath
Citation Index�, and Current Contents�/Physical, Chemical &Earth Sciences. This journal is archived in Portico and in CLOCKSS.
Printed in the United States of America.∞© The paper used in this journal is acid-free and falls withinthe guidelines established to ensure permanence and durability.
10 9 8 7 6 5 4 3 2 1 21 20 19 18 17 16
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY
CONTENTS
Vol. 53, No. 4 October 2016
ARTICLES
Michael Holst, Olivier Sarbach, Manuel Tiglio, and MicheleVallisneri, The emergence of gravitational wave science: 100 years ofdevelopment of mathematical theory, detectors, numerical algorithms,and data analysis tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513
Michael Aschbacher and Bob Oliver, Fusion systems . . . . . . . . . . . . . . . . . 555
Sourav Chatterjee, An introduction to large deviations for random graphs 617
Skip Garibaldi, E8, the most exceptional group . . . . . . . . . . . . . . . . . . . . . . . . . 643
MATHEMATICAL PERSPECTIVES
Gerald L. Alexanderson, contributor Leonard F. Klosinski, Aboutthe cover: Ramanujan in bronze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673
Selected Mathematical Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681
BOOK REVIEWS
Andrew Hassell (Reviewer), Hangzhou lectures on eigenfunctions of theLaplacian, by Christopher D. Sogge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693
Lloyd N. Trefethen (Reviewer), The Princeton companion to appliedmathematics, edited by Nicholas J. Higham . . . . . . . . . . . . . . . . . . . . . . . . . . 701
INDEX TO VOLUME 53 (2016)
bulletin articles
Aganagic, Mina. String theory and math: Why this marriage may last. Mathematics and dual-
ities of quantum physics, 93Aschbacher, Michael, and Bob Oliver. Fusion systems, 555
Belolipetsky, Mikhail. Arithmetic hyperbolic reflection groups, 437
Chatterjee, Sourav. An introduction to large deviations for random graphs, 617Fløystad, Gunnar, Jason McCullough, and Irena Peeva. Three themes of syzygies, 415
Garibaldi, Skip. E8, the most exceptional group, 643
Holst, Michael, Olivier Sarbach, Manuel Tiglio, and Michele Vallisneri. The emergence of gravita-tional wave science: 100 years of development of mathematical theory, detectors, numerical
algorithms, and data analysis tools, 513
Kuchment, Peter. An overview of periodic elliptic operators, 343McCullough, Jason. See Fløystad, Gunnar
Nahmod, Andrea R. The nonlinear Schrodinger equation on tori: Integrating harmonic analysis,geometry, and probability, 57
Okounkov, Andrei. Limit shapes, real and imagined, 187
Oliver, Bob. See Aschbacher, MichaelPeeva, Irena. See Fløystad, Gunnar
Penner, R. C. Moduli spaces and macromolecules, 217
Sarbach, Olivier. See Holst, MichaelTiglio, Manuel. See Holst, Michael
Vallisneri, Michele. See Holst, Michael
Weinstein, Jared. Reciprocity laws and Galois representations: recent breakthroughs, 1Wright, Alex. From rational billiards to dynamics on moduli spaces, 41
Zakharevich, Inna. Perspectives on scissors congruence, 269
mathematical perspectives
Alexanderson, Gerald L., and Leonard F. Klosinski. About the cover: Gauss and the Disquisi-
tiones Arithmeticæ, 117. About the cover: The Newton–Leibniz controversy, 295
Alexanderson, Gerald L., contributor Leonard F. Klosinski. About the cover: Ramanujan inbronze, 673
Klosinski, Leonard F. See Alexanderson, Gerald L.
Oswald, Nicola M. R., and Jorn Steuding. About the cover: Zeta-functions associated with qua-dratic forms in Adolf Hurwitz’s estate, 477
Steuding, Jorn. See Oswald, Nicola M. R.
book reviews
Bates, Daniel J., Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler. Nu-
merically solving polynomial systems with Bertini, reviewed by Henry Schenck, 179Brudnyi, Alexander, and Yuri Brudnyi. Methods of geometric analysis in extension and trace
problems. Volume 1, reviewed by Garving K. Luli, 143. Methods of geometric analysis in extension and trace problems. Volume 2, reviewed by
Garving K. Luli, 143Brudnyi, Yuri. See Brudnyi, Alexander
Grebert, B., and T. Kappeler. The defocusing NLS equation and its normal form, reviewed byDario Bambusi, 337
Hales, Thomas C. Dense sphere packings: a blueprint for formal proofs, reviewed by Jeffrey C.
Lagarias, 159Hauenstein, Jonathan D. See Bates, Daniel J.
Higham, Nicholas J., editor. The Princeton companion to applied mathematics, reviewed byLloyd N. Trefethen, 701
Iwaniec, H. Lectures on the Riemann zeta function, reviewed by Brian Conrey, 507
Jean, Frederic. Control of nonholonomic systems: from sub-Riemannian geometry to motionplanning, reviewed by I. Zelenko, 151
Kappeler, T. See Grebert, B.
INDEX TO VOLUME 53 (2016)
Lo Bello, Anthony. Origins of mathematical words: a comprehensive dictionary of Latin, Greek,
and Arabic roots, reviewed by John Stillwell, 331
Maggi, Francesco. Sets of finite perimeter and geometric variational problems. An introductionto geometric measure theory, reviewed by Alex Iosevich, 167
Marsh, Robert J. Lecture notes on cluster algebras, reviewed by Ralf Schiffler, 325
Mazur, Joseph. Enlightening symbols: a short history of mathematical notation and its hiddenpowers, reviewed by John Stillwell, 331
Ostrovskii, M. I. Metric embeddings: bilipschitz and coarse embeddings into Banach spaces,
reviewed by Florent P. Baudier and William B. Johnson, 495Sogge, Christopher D. Hangzhou lectures on eigenfunctions of the Laplacian, reviewed by An-
drew Hassell, 693
Sommese, Andrew J. See Bates, Daniel J.Talagrand, M. Upper and lower bounds for stochastic processes, reviewed by Antonio Auffinger,
173Wampler, Charles W. See Bates, Daniel J.
Weiß, Christian. Twisted Teichmuller curves, reviewed by Thomas A. Schmidt, 313
BULLETIN( N E W S E R I E S ) OF THE
A M E R I C A N M A T H E M A T I C A L S O C I E T Y
PROVIDENCE, RHODE ISLAND USA
ISSN 0273-0979
VOLUME 53 2016
Available electronically at www.ams.org/bull/
EDITORSSusan Friedlander, Chief EditorPeter Kuchment, Book Reviews
ASSOCIATE EDITORS
Emmanuel CandesDavid Cox Richard T. DurrettMark EmbreeDaniel S. FreedEdward Frenkel Irene M. GambaMark GoreskyAndrew J. GranvilleRobert M. Guralnick Craig L. Huneke
Lisa Jeffrey Bryna Kra Steven G. KrantzBarry MazurKen OnoPhilip E. ProtterAndrew Ranicki Israel Michael Sigal Christoph M. ThieleYuri TschinkelMichael Wolf
CONSULTANTS TO THE EDITORSGerald L. AlexandersonEdward G. Dunne
Bulletin (New Series) of the American Mathematical Society
The Bulletin publishes expository articles on contemporary mathematical research writ-ten in a way that gives insight to mathematicians who may not be experts in the particulartopic. The Bulletin publishes, by invitation only, reviews of selected books in mathematicsand short articles in the “Mathematical Perspectives” section.
Submission information. See Information for Authors at the end of this issue.Publication on the AMS website. Articles are published on the AMS website
individually after proof is returned from authors and before appearing in an issue.Subscription information. Bulletin (New Series) of the American Mathematical
Society is published quarterly. It is available electronically from www.ams.org/journals/.
For paper delivery, subscription prices for Volume 53 (2016) are US$574 list, US$459.20institutional member, US$344.40 individual member, US$516.60 corporate member. Thesubscription price for members is included in the annual dues. Subscription renewalsare subject to late fees. See www.ams.org/journal-faq for more journal subscriptioninformation. If ordering the paper version, add US$5 for delivery within the UnitedStates; US$8 for delivery outside the United States.
Back number information. For back issues see www.ams.org/backvols.Subscriptions and orders should be addressed to the American Mathematical Society,
P.O. Box 845904, Boston, MA 02284-5904 USA. All orders must be accompanied by pay-ment. Other correspondence should be addressed to the American Mathematical Society,201 Charles Street, Providence, RI 02904-2294 USA.
Copying and reprinting. Individual readers of this publication, and nonprofit li-braries acting for them, are permitted to make fair use of the material, such as to copyan article for use in teaching or research. Permission is granted to quote brief passagesfrom this publication in reviews, provided the customary acknowledgment of the sourceis given. Republication, systematic copying, or multiple reproduction of any material inthis publication is permitted only under license from the American Mathematical Soci-ety. Permissions to reuse portions of AMS publication content are now being handledby Copyright Clearance Center’s RightsLink�service. For more information, please visithttp : //www.ams.org/rightslink.
Translation rights and licensed reprint requests should be sent to [email protected].
Excluded from these provisions is material for which the author holds copyright. Insuch cases, requests for permission to reuse or reprint should be addressed directly to theauthor(s). Copyright ownership is indicated in the notice in the lower right-hand cornerof the first page of each article.
Bulletin (New Series) of the American Mathematical Society (ISSN 0273-0979 (print); ISSN 1088-9485 (online)) is published quarterly by the American Mathematical Society at 201 Charles Street,Providence, RI 02904-2294 USA. Periodicals postage is paid at Providence, Rhode Island, and addi-tional mailing offices. POSTMASTER: Send address changes to Bulletin (New Series) of the AmericanMathematical Society, American Mathematical Society, 201 Charles Street, Providence, RI 02904-2294USA.
c© 2016 American Mathematical Society. All rights reserved.
This journal is indexed in Mathematical Reviews, Science Citation Index�,Science Citation IndexTM–Expanded, ISI Alerting ServicesSM, CompuMath
Citation Index�, and Current Contents�/Physical, Chemical &Earth Sciences. This journal is archived in Portico and in CLOCKSS.
Printed in the United States of America.∞© The paper used in this journal is acid-free and falls withinthe guidelines established to ensure permanence and durability.
10 9 8 7 6 5 4 3 2 1 21 20 19 18 17 16
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY
CONTENTS
Vol. 53, No. 1 January 2016
Articles
Jared Weinstein, Reciprocity laws and Galois representations: recentbreakthroughs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Alex Wright, From rational billiards to dynamics on moduli spaces . . . . . . 41
Andrea R. Nahmod, The nonlinear Schrodinger equation on tori:Integrating harmonic analysis, geometry, and probability . . . . . . . . . . . . . 57
Mina Aganagic, String theory and math: Why this marriage may last.Mathematics and dualities of quantum physics . . . . . . . . . . . . . . . . . . . . . . . . 93
Mathematical Perspectives
Gerald L. Alexanderson and Leonard F. Klosinski, About the cover:Gauss and the Disquisitiones Arithmeticæ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Selected Mathematical Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Book Reviews
Garving K. Luli (Reviewer), Methods of geometric analysis in extensionand trace problems. Volume 1, by Alexander Brudnyi and Yuri Brudnyi;Methods of geometric analysis in extension and trace problems. Volume2, by Alexander Brudnyi and Yuri Brudnyi . . . . . . . . . . . . . . . . . . . . . . . . . . 143
I. Zelenko (Reviewer), Control of nonholonomic systems: from sub-Riemannian geometry to motion planning, by Frederic Jean . . . . . . . . . . 151
Jeffrey C. Lagarias (Reviewer), Dense sphere packings: a blueprint forformal proofs, by Thomas C. Hales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Alex Iosevich (Reviewer), Sets of finite perimeter and geometric variationalproblems. An introduction to geometric measure theory, by FrancescoMaggi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Antonio Auffinger (Reviewer), Upper and lower bounds for stochasticprocesses, by M. Talagrand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Henry Schenck (Reviewer), Numerically solving polynomial systems withBertini, by Daniel J. Bates, Jonathan D. Hauenstein, Andrew J.Sommese, and Charles W. Wampler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Vol. 53, No. 2 April 2016
Articles
Andrei Okounkov, Limit shapes, real and imagined . . . . . . . . . . . . . . . . . . . . . . 187
R. C. Penner, Moduli spaces and macromolecules . . . . . . . . . . . . . . . . . . . . . . . . 217
Inna Zakharevich, Perspectives on scissors congruence . . . . . . . . . . . . . . . . . . . 269
Mathematical Perspectives
Gerald L. Alexanderson and Leonard F. Klosinski, About the cover:The Newton–Leibniz controversy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
Selected Mathematical Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
Book Reviews
Thomas A. Schmidt (Reviewer), Twisted Teichmuller curves, by ChristianWeiß . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
Ralf Schiffler (Reviewer), Lecture notes on cluster algebras, by Robert J.Marsh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
John Stillwell (Reviewer), Origins of mathematical words: a comprehensivedictionary of Latin, Greek, and Arabic roots, by Anthony Lo Bello;Enlightening symbols: a short history of mathematical notation and itshidden powers, by Joseph Mazur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
Dario Bambusi (Reviewer), The defocusing NLS equation and its normalform, by B. Grebert and T. Kappeler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
Vol. 53, No. 3 July 2016
Articles
Peter Kuchment, An overview of periodic elliptic operators . . . . . . . . . . . . . . 343
Gunnar Fløystad, Jason McCullough, and Irena Peeva, Three themesof syzygies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
Mikhail Belolipetsky, Arithmetic hyperbolic reflection groups . . . . . . . . . . . 437
Mathematical Perspectives
Nicola M. R. Oswald and Jorn Steuding, About the cover: Zeta-functions associated with quadratic forms in Adolf Hurwitz’s estate . . 477
Selected Mathematical Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
Book Reviews
Florent P. Baudier and William B. Johnson (Reviewers), Metricembeddings: bilipschitz and coarse embeddings into Banach spaces, byM. I. Ostrovskii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495
Brian Conrey (Reviewer), Lectures on the Riemann zeta function, by H.Iwaniec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507
Vol. 53, No. 4 October 2016
Articles
Michael Holst, Olivier Sarbach, Manuel Tiglio, and MicheleVallisneri, The emergence of gravitational wave science: 100 yearsof development of mathematical theory, detectors, numerical algorithms,and data analysis tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513
Michael Aschbacher and Bob Oliver, Fusion systems . . . . . . . . . . . . . . . . . 555
Sourav Chatterjee, An introduction to large deviations for random graphs 617
Skip Garibaldi, E8, the most exceptional group . . . . . . . . . . . . . . . . . . . . . . . . . . 643
Mathematical Perspectives
Gerald L. Alexanderson, contributor Leonard F. Klosinski, About thecover: Ramanujan in bronze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673
Selected Mathematical Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681
Book Reviews
Andrew Hassell (Reviewer), Hangzhou lectures on eigenfunctions of theLaplacian, by Christopher D. Sogge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693
Lloyd N. Trefethen (Reviewer), The Princeton companion to appliedmathematics, edited by Nicholas J. Higham . . . . . . . . . . . . . . . . . . . . . . . . . . 701
Editorial Board for Articles
Emmanuel CandesRichard T. DurrettDaniel S. FreedEdward FrenkelSusan Friedlander, ChairIrene M. GambaMark GoreskyAndrew J. Granville
Robert M. GuralnickBryna R. KraBarry C. MazurAndrew RanickiChristoph M. ThieleYuri TschinkelMichael Wolf
Editorial Board for Book Reviews
David CoxMark EmbreeCraig L. HunekeLisa JeffreySteven G. Krantz
Peter Kuchment, ChairKen OnoPhilip E. ProtterIsrael Michael Sigal
Consultants to the Editors
Gerald L. AlexandersonEdward Dunne
Chief Editor: Susan Friedlander
Editorial Information
Information on the backlog for this journal can be found on the AMS website startingfrom http://www.ams.org/bull.
In an effort to make articles available as quickly as possible, articles are electronicallypublished on the AMS website individually after proof is returned from authors and beforeappearing in an issue.
A Consent to Publish is required before we can begin processing your paper. After apaper is accepted for publication, the Providence office will send a Consent to Publish formto all authors of the paper. By submitting a paper to this journal, authors certify thatthe results have not been submitted to nor are they under consideration for publicationby another journal, conference proceedings, or similar publication.
Information for Authors
The Bulletin publishes expository articles on contemporary mathematical research writ-ten in a way that gives insight to mathematicians who may not be experts in the particulartopic. All articles submitted to this journal are peer reviewed. The AMS has a single-blindpeer-review process in which the reviewers know who the authors of the manuscripts are,but the authors do not have access to information on who the peer reviewers are.
The first page must consist of a short descriptive title, followed by an abstract thatsummarizes the article in language suitable for mathematicians in the general area. Thedescriptive title should be short but informative; useless or vague phrases such as “some re-marks about” or “concerning” should be avoided. The abstract should be a brief technicaldescription of the new material.
A well-written expository article will include motivating problems and examples, someindication of the historical development of the subject, and of course the results and openproblems that make it an interesting and exciting area of mathematics. In most casesproofs should be at most briefly sketched, and there should be a good bibliography whosemain aim is to help those wishing to pursue the subject further. Articles reporting onrecent mathematical research should include an introductory section addressed to nonex-perts describing the motivation, background, and significance of the results announced.
Following the statement of results, there should be a sketch of proofs that may be ad-dressed to experts, including elements of the proof which are novel. References should begiven so that an interested reader can find the details.
Each paper should include a footnote with the 2010 Mathematics Subject Classificationrepresenting the primary and secondary subjects of the article. The classifications areaccessible from www.ams.org/msc/. The Mathematics Subject Classification footnote maybe followed by a list of key words and phrases describing the subject matter of the articleand taken from it. Journal abbreviations used in bibliographies are listed in the latestMathematical Reviews annual index. The series abbreviations are also accessible fromwww.ams.org/msnhtml/serials.pdf. To help in preparing and verifying references, theAMS offers MR Lookup, a Reference Tool for Linking, at www.ams.org/mrlookup/. Whenthe manuscript is submitted, authors should supply the Editor with electronic addressesif available.
Mathematicians giving AMS lectures (Gibbs Lectures, Colloquium Lectures, and Pro-gress in Mathematics Lectures) or invited hour addresses at meetings of the Society areencouraged to write up their lectures using the guidelines for expository articles describedabove. Submissions will be reviewed by the Editorial Board for Articles, and authors willbe notified of its decision.
Book Reviews are by invitation only. The first page must include the title of thebook being reviewed; the name(s) of the author(s); publisher; city of publication; year ofpublication; number of pages, including front matter; price if known; and ISBN. Thereshould also be a footnote with the 2010 Mathematics Subject Classification representingthe primary and secondary subjects of the book under review. The classifications areaccessible from www.ams.org/msc/. To help in preparing and verifying references, theAMS offers MR Lookup, a Reference Tool for Linking, at www.ams.org/mrlookup/.
Initial submission. Authors of articles may submit manuscripts for consideration asPDF files at http://www.ams.org/peer-review/submission.pl. Manuscripts must be asingle file with images embedded. Authors will have a chance to view the manuscript anddata entered before releasing the manuscript into the system. Two-digit 2010 Mathemat-ics Subject Classification numbers are included in a pull-down menu; classifications areaccessible from http://www.ams.org/msc/. Complete author instructions are available atthe site.
Authors who cannot supply a PDF file may submit a paper copy of their manuscript toBulletin/Peer-Review Manuscript Submissions, 201 Charles Street, Providence, RI 02904-2294 USA. These submissions will be scanned into a PDF file and entered by AMS staffinto the peer-review system. All the data required in the submission form must be providedto avoid delays in publishing the manuscript.
The Bulletin Chief Editor will be notified as new submissions arrive. The Editor willcollect these submissions and assign them to subject area specialists. Queries concerningthe status of submissions could be sent to the Editor at [email protected].
Electronically prepared manuscripts. Manuscripts should be electronically pre-pared in AMS-LATEX. To this end, the Society has prepared AMS-LATEX author packagesfor each AMS publication. Author packages include instructions for preparing electronicmanuscripts, the AMS Author Handbook, samples, and a style file that generates the par-ticular design specifications of that publication series. Articles properly prepared using theAMS-LATEX style file and the \label and \ref commands automatically enable extensiveintra-document linking to the bibliography and other elements of the article for searchingelectronically on the Web.
Authors may retrieve an author package for the Bulletin of the AMS from www.ams.
org/bull/bullauthorpac.html or via FTP to ftp.ams.org (login as anonymous, enteryour complete email address as password, and type cd pub/author-info). The AMSAuthor Handbook and the Instruction Manual are available in PDF format from the authorpackage link. The author package can also be obtained free of charge by sending email [email protected] or from the Publication Division, American Mathematical Society,201 Charles Street, Providence, RI 02904-2294 USA. When requesting an author package,
please specify the publication in which your paper will appear. Please be sure to includeyour complete email address.
After acceptance. The source files for the final version of the electronic manuscriptshould be sent to the Providence office immediately after the paper has been accepted forpublication. Authors should indicate if the paper has been prepared using AMS-LATEXor AMS-TEX. Electronically prepared manuscripts can be submitted via the Web atwww.ams.org/submit-book-journal/, sent via email to [email protected], or sent onCD to the Electronic Prepress Department, American Mathematical Society, 201 CharlesStreet, Providence, RI 02904-2294 USA. When sending a manuscript electronically viaemail or CD, please be sure to include a message indicating in which publication thepaper has been accepted. Complete instructions on how to send files are included in theauthor package.
The final file of an accepted article should also be sent by email to both bulletin@math.
uic.edu and [email protected].
Electronic graphics. Comprehensive instructions on preparing graphics are availablefrom www.ams.org/authors/journals.html. A few of the major requirements are givenhere.
Submit files for graphics as EPS (Encapsulated PostScript) files. This includes graphicsoriginated via a graphics application as well as scanned photographs or other computer-generated images. If this is not possible, TIFF files are acceptable as long as they can beopened in Adobe Photoshop or Illustrator.
Authors using graphics packages for the creation of electronic art should avoid the useof any lines thinner than 0.5 points in width. Many graphics packages allow the user tospecify a “hairline” for a very thin line. Hairlines often look acceptable when proofed ona typical laser printer. However, when produced on a high-resolution laser imagesetter,hairlines become nearly invisible and will be lost entirely in the final printing process.
Screens should be set to values between 15% and 85%. Screens which fall outside of thisrange are too light or too dark to print correctly. Variations of screens within a graphicshould be no less than 10%.
AMS policy on making changes to articles after publication. Articles are pub-lished on the AMS website individually after proof is returned from authors and beforeappearing in an issue. To preserve the integrity of electronically published articles, once anarticle is individually published to the AMS website, changes cannot be made in place inthe paper. The AMS does not keep author-related information such as affiliation, currentaddress, and email address up to date after a paper is electronically published.
Corrections of critical errors may be made to the paper by submitting an errata articleto the Editor. The errata article will be published electronically, will appear in a futureprint issue, and will link back and forth on the Web with the original article.
Secure manuscript tracking on the Web. Authors can track their manuscriptsthrough the AMS journal production process using the personal AMS ID and Arti-cle ID printed in the upper right-hand corner of the Consent to Publish form sent toeach author who publishes in AMS journals. Access to the tracking system is availablefrom www.ams.org/mstrack/. An explanation of each production step is provided onthe Web through links from the manuscript tracking screen. Questions may be sent [email protected].
Inquiries. Any inquiries concerning a paper that has been accepted for publicationthat cannot be answered via the manuscript tracking system mentioned above should besent to [email protected] or directly to the Electronic Prepress Department, AmericanMathematical Society, 201 Charles Street, Providence, RI 02904-2294 USA.
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY
CONTENTS
Vol. 53, No. 4 October 2016
ARTICLES
Michael Holst, Olivier Sarbach, Manuel Tiglio, and Michele
Vallisneri, The emergence of gravitational wave science: 100 years of
development of mathematical theory, detectors, numerical algorithms,
and data analysis tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513
Michael Aschbacher and Bob Oliver, Fusion systems . . . . . . . . . . . . . . . . . 555
Sourav Chatterjee, An introduction to large deviations for random graphs 617
Skip Garibaldi, E8, the most exceptional group . . . . . . . . . . . . . . . . . . . . . . . . . 643
MATHEMATICAL PERSPECTIVES
Gerald L. Alexanderson, contributor Leonard F. Klosinski, About
the cover: Ramanujan in bronze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673
Selected Mathematical Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681
BOOK REVIEWS
Andrew Hassell (Reviewer), Hangzhou lectures on eigenfunctions of the
Laplacian, by Christopher D. Sogge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693
Lloyd N. Trefethen (Reviewer), The Princeton companion to applied
mathematics, edited by Nicholas J. Higham . . . . . . . . . . . . . . . . . . . . . . . . . . 701
Am
erican Mathem
atical Society Distribution C
enter 35 M
onticello Place, Pawtucket, R
I 02861 USA