Birds and Frogs Equation

Home , Abram Besicovitch, Calogero conjecture, Daniel Biss, John Allen Paulos, Mary Cartwright, Modular invariant theory

Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Quadratic Diophantine Multiscale Principles of Equations Finite Harmonic of the American Mathematical Society T. Andreescu, University of Texas at Element Analysis February 2009 Volume 56, Number 2 Dallas, Richardson, TX, USA; D. Andrica, Methods A. Deitmar, University Cluj-Napoca, Romania Theory and University of This text treats the classical theory of Applications Tübingen, quadratic diophantine equations and Germany; guides readers through the last two Y. Efendiev, Texas S. Echterhoff, decades of computational techniques A & M University, University of and progress in the area. The presenta- College Station, Texas, USA; T. Y. Hou, Münster, Germany California Institute of Technology, tion features two basic methods to This gently-paced book includes a full Pasadena, CA, USA investigate and motivate the study of proof of Pontryagin Duality and the quadratic diophantine equations: the This text on the main concepts and Plancherel Theorem. The authors theories of continued fractions and recent advances in multiscale finite emphasize Banach algebras as the quadratic fields. It also discusses Pell’s element methods is written for a broad cleanest way to get many fundamental Birds and Frogs equation. audience. Each chapter contains a results in harmonic analysis. simple introduction, a description of page 212 2009. Approx. 250 p. 20 illus. (Springer proposed methods, and numerical 2009. Approx. 345 p. (Universitext) Monographs in Mathematics) Softcover examples of those methods. Softcover ISBN 978-0-387-35156-8 ISBN 978-0-387-85468-7 $49.95 approx. $59.95 2009. X, 234 p. (Surveys and Tutorials in The Strong Free Will the Applied Mathematical Sciences) Solving Softcover Theorem Introduction to Siegel the Pell Modular Forms and ISBN: 978-0-387-09495-3 $44.95 Equation page 226 Dirichlet Series Intro M. J. Jacobson, Jr., A. Andrianov, Russian Academy of the duction to H. C. Williams, Sciences, Petersburg Department of the Boolean University of Steklov Institute of Mathematics, Calgary, AB, St. Petersburg, Russia Algebras Canada San Francisco This is intended for a graduate course S. Givant, Mills The authors provide a friendly Meeting on Siegel modular forms, Hecke College, Oakland, introduction to algebraic number operators, and related zeta functions. CA, USA; P. Halmos, theory via Pell’s Equation. The only page 324 The author’s aim is to present a concise deceased prerequisites are knowledge of and self-contained introduction to a This book is an informal though elementary number theory and abstract developing area of number theory that systematic series of lectures on Boolean algebra. Volume 56, Number 2, Pages 201–336, February 2009 will serve to attract young researchers algebras. It contains background Worcester Meeting to this field. chapters on topology and continuous 2009. Approx. 520 p. 20 illus. (CMS Books functions and includes hundreds of in Mathematics) Hardcover page 326 2009. XII, 184 p. (Universitext) Softcover exercises as well as a solutions manual. ISBN 978-0-387-84922-5 $79.95 ISBN 978-0-387-78752-7 $59.95 2009. XIV, 574 p. 10 illus. (Undergraduate Texts in Mathematics) Hardcover ISBN 978-0-387-40293-2 $59.95

Learn about our eBook Collection in Mathematics and Statistics. Talk to your Librarian Today

Easy Ways to Order for the Americas Write: Springer Order Department, PO Box 2485, Secaucus, NJ 07096-2485, USA Call: (toll free) 1-800-SPRINGER Fax: 1-201-348-4505 Email: [email protected] or for outside the Americas Write: Springer Customer Service Center GmbH, Haberstrasse 7, 69126 Heidelberg, Germany Call: +49 (0) 6221-345-4301 Fax : +49 (0) 6221-345-4229 Email: [email protected] Prices are subject to change without notice. All prices are net prices. 014032x Long divide (see page 239)

Trim: 8.25" x 10.75" 136 pages on 40 lb Cougar Opaque • Spine: 3/16" • Print Cover on 9pt Carolina ,!4%8

,!4%8 ,!4%8 Volume 2008 Open Access Journals Abstract andApplied Analysis in Mathematics

Your research wants to be free!

Hindawi Publishing Corporation http://www.hindawi.com

Advances in Difference Equations

Advances in Mathematical Physics Submit your manuscripts at Hindawi Publishing Corporation http://www.hindawi.com Volume 2008 Hindawi Publishing Corporation Volume 2008 http://www.hindawi.com http://www.hindawi.com

7 Volume 2008 6 Advances in Discrete Dynamics in 9 5 Operations Nature and Society 1 8 Boundary An International Multidisciplinary Research and Review Journal Research Value 7 Problems 6 Differential Equations 7 and Nonlinear Advances in Mechanics

Numerical Analysis Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation3 Volume 2008 Hindawi Publishing Corporation http://www.hindawi.com Volume 2008 Hindawi Publishing Corporation http://www.hindawi.com 2 http://www.hindawi.com Volume 2008 http://www.hindawi.com http://www.hindawi.com Volume 2008

Fixed Point Theory International Journal of and Applications Journal of Applied Mathematics Mathematics and Mathematical Sciences

International Journal of International Journal of Differential Combinatorics Equations Hindawi Publishing Corporation http://www.hindawi.com Volume 2008 Hindawi Publishing Corporation Volume 2008 Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com http://www.hindawi.com Volume 2008 http://www.hindawi.com Volume 2008 http://www.hindawi.com Volume 2008

Journal of Journal of Journal of Mathematical Applied JAMSA Inequalities Probability and Applications Problems in Mathematics and Journal of Applied Mathematics Engineering and Stochastic Analysis and Statistics Theory, Methods, and Applications Decision Sciences

Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2008 Hindawi Publishing Corporation http://www.hindawi.com Volume 2008 http://www.hindawi.com Volume 2008 http://www.hindawi.com Volume 2008 http://www.hindawi.com Volume 2008 New and Forthcoming

Algebra, Arithmetic, and Arithmetic and Geometry Symmetry and Spaces Geometry around Quantization In Honor of Gerry Schwarz In Honor of Y.I. Manin Ozgur Ceyhan; Yuri I. Manin; H.E.A. Campbell, Memorial University Matilde Marcolli, Max-Planck Institut, of Newfoundland, St. John‘s, NF, Yuri Tschinkel, New York University, Bonn, Germany (Eds.) Canada; Loek Helminck, North Carolina New York, NY, USA; Yuri G. Zarhin, State University, Raleigh, NC, USA; Pennsylvania State University, University Quantization has been a potent source Hans-Peter Kraft, Universität Basel, Park, PA, USA (Eds.) of interesting ideas and problems in Switzerland; David Wehlau, Queen‘s various branches of mathematics. This Contributors include: K. Behrend, University, Kingston, ON, Canada (Eds.) volume comprises both research and V. Berkovich, J.-B. Bost, P. Bressler, survey articles originating from the This volume covers the wide range of D. Calaque, J. Carlson, A. Chambert-Loir, conference on Arithmetic and Geometry mathematics to which Gerry Schwarz has E. Colombo, A. Connes, C. Consani, around Quantization held in Istanbul in either made fundamental contributions A. Dabrowski, C. Deninger, I. Dolgachev, 2006. A wide range of topics related to or stimulated others to pursue. Three S. Donaldson, T. Ekedahl, A.-S. Elsenhans, quantization are covered, thus aiming to papers examine various aspects of B. Enriquez, P. Etingof, V. Fock, give a glimpse of a broad subject in very modular invariant theory (Broer, Elmer and E. Friedlander, B. Geemen, E. Getzler, different perspectives. Fleischmann, Shank and Wehlau), and A. Goncharov, M. Harris, I. Iskovskikh, Contributors: S. Akbulut, S. Arkhipov, seven papers concentrate on characteristic J. Jahnel, D. Kaledin, M. Kapranov, Ö. Ceyhan, E. Frenkel, K. Fukaya, 0 (Brion, Daigle and Freudenberg, Greb N. Katz, R. Kaufmann, J. Kollár, D. Gaitsgory, S. Gurevich, R. Hadani, and Heinzner, Helminck, Kostant, Kraft and M. Kontsevich, E. Looijenga, M. Marcolli, K. Kremnizer, S. Mahanta, S. Salur, Wallach, Traves). M. Markl, L. Merel, S. Merkulov, G. Ben Simon, W. van Suijlekom. M. Movshev, E. Mukhin, J. Nekovar, 2009. APPROX. 220 P. HARDCOVER V. Nikulin, F. Oort, D. Orlov, A. Panchishkin, 2009. APPROX. 400 P. HARDCOVER ISBN 978-0-8176-4874-9 CA. $99.00 I. Penkov, A. Polishchuk, P. Sarnak, ISBN 978-0-8176-4830-5 CA. $129.00 PROGRESS IN MATHEMATICS V. Schechtman, O. Ogievetsky, PROGRESS IN MATHEMATICS A. Tikhomirov, B. Tsygan, G. van der Geer, Frobenius Categories E. Vasserot, A. Vishik, A. Voronov, Developments and Trends M. Wodzicki, Y. Zarhin, T. Zink versus Brauer Blocks in Infinite-Dimensional VOL. I: 2009. APPROX. 600 P. HARDCOVER The Grothendieck Group ISBN 978-0-8176-4744-5 CA. $99.00 Lie Theory of the Frobenius Category PROGRESS IN MATHEMATICS, VOL. 269 Karl-Hermann Neeb, Darmstadt University of a Brauer Block of Technology, Germany; Arturo Pianzola, Lluis Puig, Université Paris VII Denis VOL. II: 2009. APPROX. 600 P. HARDCOVER University of Alberta, Canada (Eds.) Diderot, Paris, France ISBN 978-0-8176-4746-9 CA. $99.00 This collection of invited expository papers PROGRESS IN MATHEMATICS, VOL. 270 This book examines important questions focuses on recent developments and in modern representation theory of fi nite trends in infi nite-dimensional Lie theory, Observation and Control groups. On the one hand, it introduces and which has become one of the core areas develops the abstract setting of Frobenius for Operator Semigroups of modern mathematics. The book is di- categories (also called Saturated fusion vided into three parts: infi nite-dimensional Marius Tucsnak, Université Nancy, France; systems), created by the author fi fteen Lie (super-)algebras, geometry of infi nite- George Weiss, Tel Aviv University, Israel years ago for a better understanding of dimensional Lie (transformation) groups, what was loosely called the local theory This book studies observation and control and representation theory of infi nite-dimen- of fi nite groups or blocks, and for the operators for linear systems, in which sional Lie groups. purpose of an eventual classifi cation. On the free evolution of the state can be Contributors include: B. Allison, D. Beltita, the other hand, it presents the application described by an operator semigroup on a W. Bertram, J. Faulkner, Ph. Gille, of the abstract setting to the blocks. In Hilbert space. Emphasized in the text are H. Glöckner, K-H. Neeb, E. Neher, particular, it develops a framework for a well-posedness, observability and control- I. Penkov, A. Pianzola, D. Pickrell, deeper understanding of one of the central lability properties. The abstract results are T. Ratiu, N. Scheithauer, C. Schweigert, open problems in representation theory, supported by a large number of detailed V. Serganova, K. Styrkas, K. Waldorf, known as Alperin’s Weight Conjecture examples coming mostly from partial dif- and J. Wolf. ferential equations. (AWC). 2009. APPROX. 430 P. HARDCOVER 2009. APPROX. 510 P. HARDCOVER 2009. APPROX. 475 P. HARDCOVER ISBN 978-0-8176-4740-7 CA. $79.95 ISBN 978-3-7643-9997-9 $109.00 ISBN 978-3-7643-8993-2 $79.95 PROGRESS IN MATHEMATICS BIRKHÄUSER ADVANCED TEXTS PROGRESS IN MATHEMATICS, VOL. 274 CALL: 1-800-777-4643 • FAX: (201) 348-4505 • E-MAIL: [email protected] • www.birkhauser.com Please mention promotion #014044 when ordering. Prices are valid in the Americas only and are subject to change without notice. For price and ordering information outside the Americas, please contact Birkhäuser Verlag AG by E-mail: [email protected] 014044x Notices 233 226 of the American Mathematical Society February 2009

Communications

224 Mathematics Research Communities Program 224 Kicks Off Allyn Jackson

240 WHAT IS…a Skein Module? W. B. Raymond Lickorish

244 Tribute to André Lichnerowicz (1915–1998) Yvette Kosmann- Schwarzbach

247 Presidential Views: Interview with James Features Glimm Allyn Jackson 212 Birds and Frogs 250 Ask Professor Nescio Freeman Dyson 253 A Clicker Approach to The author calls mathematicians who take a lofty Teaching Calculus conceptual view of their subject birds and those who Martina Bode, Denise work in details and solve their problems consecutively Drane, Yifat Ben-David frogs. The author shows, by examples from the past Kolikant, and Mary Schuller and his personal acquaintance, how both types have 257 2008 Annual Survey of the advanced mathematics. Mathematical Sciences 226 The Strong Free Will Theorem (First Report) Polly Phipps, James W. John H. Conway and Simon Kochen Maxwell, and Colleen Rose The authors prove that three of the basic axioms of Commentary relativity and quantum mechanics have the consequence that the response of a certain type of particle 207 Opinion: A Mathematician to a certain type of experiment is independent of the Runs for Political Office universe prior to this response. Or, as the authors Daniel Biss put it, “If humans have free will [in choosing the 209 oLetters t the Editor orientation for the apparatus in the experiment], then elementary particles…share this valuable commodity.” 233 Mathematics and the Aesthetic—A Book Review Reviewed by Annalisa Crannell

237 Group Theory in the Bedroom—A Book Review Reviewed by David Austin Notices Departments of the American Mathematical Society About the Cover...... 239 EDITOR: Andy Magid Mathematics People ...... 268 ASSOCIATE EDITORS: Daniel Biss, Susanne C. Brenner, Bill Casselman Srinivas Receives TWAS Prize in Mathematics, Pujals Awarded ICTP/IMU (Graphics Editor), Robert J. Daverman, Susan Ramanujan Prize, Strassen Awarded ACM Knuth Prize, Ozawa Receives Friedlander, Robion Kirby, Steven G. Krantz, Lisette de Pillis, Peter Sarnak, Mark Saul, John Operator Algebra Prize, Saaty Receives INFORMS Award, Vybiral Swallow, Lisa Traynor Receives 2008 Information-Based Complexity Young Researcher Award, SENIOR WRITER and DEPUTY EDITOR: DMV Media Prizes, NSF Career Awards Made, Royal Society of London Allyn Jackson Elections, Kenneth M. Hoffman (1930–2008), Marcia P. Sward (1939– MANAGING EDITOR: Sandra Frost 2008), Correction. CONTRIBUTING WRITER: Elaine Kehoe Mathematics Opportunities...... 272 PRODUCTION ASSISTANT: Muriel Toupin Mathematics Research Communities 2009, NSF Program ADVANCE, PRODUCTION: Kyle Antonevich, Stephen Moye, Erin Murphy, Lori Nero, Karen Ouellette, Donna Salter, NSF Partnerships for International Research and Education, Summer Deborah Smith, Peter Sykes, Patricia Zinni Program for Women Undergraduates, NSF Support for Undergraduate ADVERTISING SALES: Anne Newcomb Training in Biological and Mathematical Sciences, Nominations for Information-Based Complexity Prize 2009. SUBSCRIPTION INFORMATION: Subscription prices for Volume 56 (2009) are US$488 list; US$390 insti- Inside the AMS...... 274 tutional member; US$293 individual member. (The From the AMS Public Awareness Office, AMS Email Support for subscription price for members is included in the annual dues.) A late charge of 10% of the subscrip- Frequently Asked Questions, Deaths of AMS Members. tion price will be imposed upon orders received from nonmembers after January 1 of the subscription year. Reference and Book List...... 276 Add for postage: Surface delivery outside the United States and India—US$27; in India—US$40; expedited delivery to destinations in North America—US$35; Doctoral Degrees Conferred (2007–2008) ...... 281 elsewhere—US$88. Subscriptions and orders for AMS publications should be addressed to the American Mathematics Calendar ...... 307 Mathematical Society, P.O. Box 845904, Boston, MA 02284-5904 USA. All orders must be prepaid. New Publications Offered by the AMS...... 311 ADVERTISING: Notices publishes situations wanted and classified advertising, and display advertising for publishers and academic or scientific organizations. Classified Advertisements...... 320 Advertising material or questions may be sent to [email protected] (classified ads) or notices-ads@ Meetings and Conferences of the AMS...... 322 ams.org (display ads). SUBMISSIONS: Articles and letters may be sent to Meetings and Conferences Table of Contents...... 335 the editor by email at [email protected], by fax at 405-325-5765, or by postal mail at Department of Mathematics, 601 Elm, PHSC 423, University of Okla- homa, Norman, OK 73019-0001. Email is preferred. Correspondence with the managing editor may be sent to [email protected]. For more information, see the section “Reference and Book List”. NOTICES ON THE AMS WEBSITE: Supported by the AMS membership, most of this publication is freely available electronically through the AMS website, the From the Society’s resource for delivering electronic products and services. Use the URL http://www.ams. AMS Secretary org/notices/ to access the Notices on the website. [Notices of the American Mathematical Society (ISSN 0002- 9920)s i published monthly except bimonthly in June/July Applications and Nominations Sought for AMS Associate by the American Mathematical Society at 201 Charles Street, Providence, RI 02904-2294 USA, GST No. 12189 2046 RT****. Treasurer ...... 303 Periodicals postage paid at Providence, RI, and additional mailing offices. POSTMASTER: Send address change notices 2008 Election Results ...... 304 to Notices of the American Mathematical Society, P.O. Box 6248, Providence, RI 02940-6248 USA.] Publication here of the Society’s street address and the other information in brackets 2009 AMS Election (Nominations by Petition) ...... 305 above is a technical requirement of the U.S. Postal Service. Tel: 401-455-4000, email: [email protected]. © Copyright 2009 by the American Mathematical Society. All rights reserved. Printed in the United States of America.The paper used in this journal is acid-free and falls within the guidelines established to ensure permanence and durability.

Opinions expressed in signed Notices articles are those of the authors and do not necessarily reflect opinions of the editors or policies of the American Mathematical Society. A M E R I C A N M ATHEMATICAL S OCIETY

Mathematical Improving Stents Getting It Together

Stents are expandable tubes that are inserted into blocked The collective motion of many groups of animals can be stun- or damaged blood vessels. They offer a practical way to treat ning. Flocks of birds and schools of fish are able to remain coronary artery disease, repairing vessels and keeping them cohesive, find food, and avoid predators without leaders and open so that blood can flow freely. When stents work, they without awareness of all but a few other members in their are a great alternative to radical surgery, but they can dete- groups. Research using vector analysis and statistics has led riorate or become dislodged. Mathematical models of blood to the discovery of simple principles, such as members main- vessels and stents are helping to determine better shapes and taining a minimum distance between neighbors while still materials for the tubes. These models are so accurate that the aligning with them, which help explain shapes such as the one FDA is considering requiring mathematical modeling in the below. Moments design of stents before any further testing is done, to reduce the need for expensive experimentation. A series of over 70 posters that describe the role mathematics plays in science, nature, technol- Photo by Jose Luis Gomez de Francisco. Image courtesy of Michel Leconte. ogy, and human culture. Some have been trans- The Mathematical Moments program promotes The Mathematical Moments program promotes appreciation and understanding of the role mathematics appreciation and understanding of the role mathematics plays in science, nature, technology, and human culture. plays in science, nature, technology, and human culture. lated into other languages, and some feature MM/72.s www.ams.org/mathmoments MM/68.s www.ams.org/mathmoments podcast interviews with experts in the field. Listen Up! — Podcast Interviews with Experts

Diandra L. Leslie-Pelecky, University of Texas at Dallas, on the math-

ematics of NASCAR Leslie-Pelecky Golden Ken Golden, University of Utah, on the mathematics of sea ice Kevin Short, University of New Hampshire, on digitizing a wire recording of Woodie Guthrie (and his resulting Grammy© Award) Tim Chartier, Davidson College, on the connections between mathematics and soccer

and more... Short Chartier

Mathematical Moments in Other Languages Read translated versions in Chinese, Spanish, French, German, Portuguese, Polish, Japanese, and Russian.

Using Mathematical Moments

• Display in your office • Use in the classroom • Distribute at special events • Promote math to colleagues • Post on bulletin boards • Launch a math club activity www.ams.org/mathmoments WebAssign ad Notices 8/13/07 12:40 PM Page 1

“THE PROOF IS IN OUR STUDENTS’ GRADES. WEBASSIGN WORKS.” Michael Paesler Department Head

With over a million users and half a billion submissions, WebAssign is the leading online homework and grading solution for math and science. But what makes us most proud of WebAssign is what department heads and chairs like Michael Paesler are saying about its impact on students and faculty. “The greatest advantage is that our students get immediate feedback on their work, and my faculty have more time for teaching and helping their students learn instead of grading innumerable homework papers. My professors recently found that more than 90% of their introductory students successfully completed every assignment using WebAssign. That’s impressive!” So if you’re wondering why you should consider WebAssign for your students, the answer is simple: WebAssign works.

The way you imagined teaching could be.™

800.955.8275 webassign.net Opinion

and learning about a billion new things. If you’re read- A Mathematician Runs ing this magazine, you’ve probably always been good at homework. Your campaign (as well as the preparation time for Political Office you spend figuring out how your campaign will work) is a great time to dust off that skill. As I sit down to write this essay, just over a week has 5. But don’t be a big jerk. When I announced my can- elapsed since my narrow defeat in the 2008 election. I didacy, one of my mathematical colleagues expressed was the Democratic nominee for State Representative in concern that it would be hard to move out of mathemat- the (north suburban Chicago) 17th District of Illinois. Not ics, where everyone was “really smart”. Aside from being many mathematicians run for office, but as interest in an obnoxious sentiment, it’s totally wrong. There are energy, environmental, and technology policy increases, reasons I’ve missed being a mathematician, but access more people with scientific backgrounds are consider- to bright people and interesting conversation sure isn’t ing this professional transition. In Illinois, I’m happy among them. to say that this is a bipartisan phenomenon, thanks to 6. In fact, if you do this correctly, you’ll learn more Democratic Congressman Bill Foster and Republican State than in any other phase of your life. A political campaign Representative Mike Fortner, both particle physicists. is an extremely complicated machine, made up of dozens Given my vantage point, I thought it might be useful to of moving parts and thousands of people. You’ll encoun- offer some insights and suggestions for mathematicians ter more different ideas and tasks than you can possibly considering politics. imagine. It’s scary and difficult, but truly inspiring. 1. You have an important advantage. You’ve probably 7. One thing you’ll learn how to do is cut corners. been struck by how often candidates use the phrase “solv- A campaign inevitably involves a lot of corner-cutting. ing problems”. This is partially because “solving problems” Over 70,000 voters reside in our district, and 52,418 of is a kind of antonym of “partisan bickering”, making it them cast a ballot in my race. The ideal campaign would a particularly salient concept in 2008’s Obama-driven involve talking individually with each one for at least half political culture. There’s another reason, though: when an hour. Obviously, I didn’t have 25,000 hours. The main done correctly, policymaking involves solving technical purpose of a campaign is to short-circuit that process but problems by analyzing data and predicting consequences still deliver substantive communication. of various actions. This data-driven approach to policy- 8. You’ll also get a visceral education about long tails. making is sorely missed today. (And while the Bush admin- If you’re running in a district smaller than a Congressional istration elevated throwing out the data to a grotesque art district and you want to win, then you’ll knock on doors. form, this practice did not begin in 2001 and is unfortu- Lots of them. (I knocked on over 20,000.) This will be one nately not limited to the executive branch of government.) of the most valuable experiences of your life—you’ll learn If you’re reading this magazine, chances are you actually so much about your community and human nature. But solve problems for a living; in other words, you’re more because of the law of large numbers, you’ll also have a fair justified than almost anyone in calling yourself a problem- number of extraordinary experiences. Besides the naked solver. Voters get this, and they like it. man in the wheelchair (really) and the horrifying racist, 2. You have another important advantage. If you’re you’ll also encounter your fair share of human stories of reading this magazine, you’re also probably a teacher. struggle. You’ll find yourself hugging, laughing, and cry- That means you speak in public several days a week. More- ing with a lot more strangers than you can imagine. It’s over, you do so in circumstances far less favorable than truly uplifting. those confronting politicians most days (they talk for ten 9. But never forget this is still politics. When I began minutes, not an hour, about subject matter that—and it running, some friends worried that I was entering this pains me to say this—most people find less boring than slimy world of character assassination. I replied “Sure, mathematics). By Election Day, I’d become a pretty good that’s how politics looks on TV, but I’m not running for political speaker, based only on my experience in the president. A local campaign will be much more civil.” Just classroom, my passion about the issues, and a lot of hard days before the election, a letter was sent to voters level- work. You can too. ing completely fabricated accusations, urging recipients 3. You have yet another important advantage. Your to vote for my opponent, and describing such an action schedule is flexible. The number of hours you’re in class as “a vote against the very worst in politics”. The letter is quite a bit lower than most people’s time commitment. concluded by asking people to call me to express their Your summer vacation is auspiciously scheduled shortly outrage, and listed my cell phone number. before the first Tuesday after the first Monday in Novem- 10. Speaking of my cell phone number, it’s 773-383- ber—squeeze everything you can out of it. Naturally, you 6774. I hope you’ll consider running for office, and if have other duties, like research and class preparation, and you do, please call me. I’d love to help! (Unless you’re a you need to fulfill those duties responsibly. Just make sure Republican, in which case Fortner would probably be a you don’t spend time on them while voters and donors better bet.) are awake. —Daniel Biss 4. And you have one more important advantage. Run- Evanston, Illinois ning for office is really hard and involves tons of work [email protected]

February 2009 Notices of the AMS 207 American Mathematical Society

Fan China Exchange Program

Grants to support collaborations between Chinese and U.S./Canadian researchers are made possible through the generosity of Ky and Yu-Fen Fan.

The Fan China Exchange Program is intended to send eminent mathematicians from the U.S. and Canada to make a positive impact on the mathematical research community in China and to bring Chinese scientists in the early stages of their research to the U.S. and Canada to help further their careers. The program encourages host institutions to provide some type of additional support for the travel or living expenses of the visitor and to ensure a suitable length of stay.

Applications received before March 15 will be considered for the following academic year.

For more information on the Fan China Exchange Program and application process see www.ams.org/employment/chinaexchange.html or contact the AMS Membership and Programs Department by telephone at 800-321- 4267, ext. 4170 (U.S. and Canada), or 401-455-4170 (worldwide), or by email at [email protected]. Letters to the Editor

Imperfect Mathematics and a foreign member of the AMS 2005 465 493 507 A thought on Melvyn B. Nathanson’s (since the late 1970s). 2006 490 503 514 August 2008 Opinion piece “Desper- 2007 500 500 500 Salary Trends ately seeking truth”: The wage-adjusted figures show Just like our lines are not infinitely The Annual Survey compares the a downward trend (after 1990) that straight and our points are not infi- starting salaries of new Ph.D.’s over is not apparent in the COL-adjusted nitely thin, so too our journals and the years by giving their (median, numbers. our refereeing process are only rough quartiles, etc.) annual salaries in past —Seymour Haber approximations of the idealized no- years both in then-current dollars Temple University (Emeritus) tions they are supposed to represent. and in 2007 dollars. This adjustment [email protected] This is, after all, mathematics done is made via the Cost-of-Living (COL) by humans. index and shows what has happened (Received November 8, 2008) —Gabriel Nivasch to the real purchasing power of start- Tel Aviv University ing salaries over time. [email protected] There is another way to adjust Mathematics Education for salaries to the changing environment Girls (Received November 2, 2008) that gives additional information. The article “Cross-cultural analysis That is to adjust them by the Average of students with exceptional talent Wage Index. For example the AWI for in mathematical problem solving” Citation Statistics Report 2007 was US$40,405 while that for [November 2008 Notices] reminded Citation 1990 was US$21,028. Their ratio is me of how, back in the USSR, ev- I am sorry to report to you that the 1.92. Thus a salary of US$32,000 in eryone claimed that the Soviets had footnote on page 1221 in the Novem- 1990 would rank roughly like one of the best math schools in the world. ber 2008 Notices is misleading, and US$61,500 in 2007. (By “rank” I mean The widely-accepted explanation was quite unfair. its position in the scale of salaries. that every person who was gifted in The Citation Statistics report is not It would be better to give the actual technical fields had no choice but to an IMU [International Mathematical percentile, but I don’t have those become a scientist. Indeed, neither Union] report. It is a joint IMU-ICIAM- figures.) private business nor the stock market IMS report and should be quoted as The rank of one’s salary in the gen- existed in the USSR. Lawyers didn’t such. [ICIAM = International Council eral salary population is significant. need any gifts, other than the ability for Industrial and Applied Mathemat- It largely determines in which neigh- to obey. The only way to get a hefty ics, IMS = Institute of Mathematical borhoods one can afford to live, and salary was to become a big manager, Statistics]. the figures for the whole Ph.D. group and for this you had to sell your soul This is all the more distressing as may perhaps indicate the changes in by joining the Communist Party. the AMS is an associate member of the value society places on our pro- On the other hand, if you had a ICIAM, whereas it is not a member fession. The following table shows Ph.D., you would get a sizable bonus. of the IMU. Also, the presence of the the median starting salaries for new Hence, every gifted person tried to IMS as a co-sponsor lends even more Ph.D.’s taking 9–10-month academic enter the prestigious world of science weight and credence to such a report teaching/teaching-and-research posi- and mathematics. No wonder the on statistics. tions. The second and third columns Soviet math tradition and math edu- Thank you for making the proper are from p. 822 in the August 2008 cation was so good. Can you imagine corrections, including on the AMS Notices; they give the salaries in cur- what would happen to math educa- website. rent and in 2007 dollars respectively. tion in the U.S. if energetic and am- To spread the guilt a little, note The fourth column gives the salaries bitious people like Google founders that there are many websites which adjusted to the AWI (all in hundreds Larry Page and Sergey Brin decided to make the same mistake, including of dollars). become math educators? SIAM’s, even when SIAM is a founding I do think that math education member of ICIAM! 1980 171 379 552 here in the U.S. is a disaster. But it —Alain Damlamian 1985 250 429 600 would be a bigger disaster to try to Université Paris-Est 1990 320 469 614 improve it by following the commu- (Paris-12 Val de Marne) 1995 350 455 579 nism path. Let’s find another way. [email protected] 2000 415 497 523 In examining the data in this article, it appears that girls in Com- (Received November 6, 2008) 2001 420 491 517 munist countries are doing better in 2002 450 517 547 math competitions than American Editor’s Note: The author is past 2003 450 506 536 girls. We are supposed to be the secretary of ICIAM (1999–2007), 2004 450 491 508 democratic leaders around gender

February 2009 Notices of the AMS 209 Letters to the Editor equality issues, but why then are survival salaries under demeaning pertaining to his emigration to the our young women mathematicians conditions. United States during World War II, behind? I was gratified to see the AMS Despite the often difficult circum- his wartime employment search, and addressing this concern. I also started stances of his life, Loewner produced attempts to determine the where- exploring issues around women and an impressive body of original work abouts of his family remaining in math on my blog at http://blog. that left permanent imprints on math- Europe. This accession also contains tanyakhovanova.com/?cat=17. ematical thinking, in a wide range of academic records and correspon- —Tanya Khovanova directions. He published little, but dence to and from colleagues at the MIT each work that appeared was on a many academic institutions where [email protected] level to change the direction of math- Loewner taught including the Univer- ematics. Much of his contribution was sity of Louisville, Brown University, (Received November 22, 2008) offered in informal conversation with Syracuse University, and Stanford students and colleagues; he shared University. Other items include photographs, publishing contracts, me- Editor’s Note: The author was a mem- everything, and fruits of his talent ap- morial tributes to Loewner and his ber of the USSR IMO team (1975 pear in many publications by others. wife Elizabeth, and news clippings silver medal; 1976 gold medal). His central interest was geometric function theory, to which he applied about the Loewner family. Notes: variational methods. Using strikingly Charles Loewner was born on May Loewner Archive Established original reasoning, he proved the 29, 1893, in Lany, Bohemia (now in the Czech Republic), and received his We are writing to convey to the math- initial case for the Bieberbach Con- jecture, and the ideas of that proof Promotion (Ph.D.) in Mathematics at ematical community that profes- the (German) Charles University in sional and personal documents from were central to the later complete proof by de Branges. He was inter- Prague. From 1922–1928 he taught the legacy of Charles Loewner, which at Friedrich Wilhelm University in were donated to Stanford University ested also in fluid flow problems, in which his geometric thinking had Berlin. Following a brief lectureship at by his daughter Marian Tracy, have Cologne, he returned to the (German) been organized and catalogued and great influence. His thinking led him to the general study of semi-groups Charles University as Ausserordentli- are part of the Stanford University of transformations, for which again cher Professor (associate professor) Archives located in the Stanford Uni- and was later promoted to Ordinarius there were remarkable consequences versity Libraries. The online guide (full professor). The occupation of in several directions, with unexpected can be accessed at http://content. Czechoslovakia in 1939 prompted physical applications. cdlib.org/view?docId=kt7c6037b his emigration to the United States. Loewner was also famous for his h&brand=oac. He taught at Louisville, Brown, and interaction with students at all levels. Those wishing to view the material Syracuse University prior to his ap- His lectures were polished and per- should contact publication staff in the pointment in 1951 as professor of fect, presented without notes; they at- Department of Special Collections and mathematics at Stanford University, tracted students and also professors. University Archives, at speccolref@ where he remained until his death His problem seminar at Stanford was stanford.edu. on January 8, 1968. Indexes: Unpub- celebrated, and became a birthplace lished guide available (folder level in- Many of the current readers will of inspiration leading to Ph.D. dis- ventory). Notes: Gift of Marian Tracy, have arrived too recently on the sertations, for many students. mathematical scene to be directly im- 2007/1972. Subject (LC): Loewner, For the convenience of readers, we Charles, 1893–1968. pacted as we have been by Loewner’s are enclosing below a brief summary profound insights and originality, of the material. —Robert Finn by his selfless human qualities, and Physical Description: 4.5 linear by the depth and universality of his [email protected] ft. Summary: The first seven boxes scientific contributions. Beyond those of this collection consist largely of —Robert Osserman comments, his life experiences as a Loewner’s lectures notes, 1923–1956, [email protected] Jewish refugee who barely escaped with some exams and class projects; Department of Mathematics the Nazi holocaust, and who lost manuscripts and typescripts of ar- Stanford University close family members in those horrid ticles, 1919–62, including his 1933 events, reflect poignantly the sweep- thesis; and research notes and writ- (Received November 25, 2008) ing social changes and the terrible ings. Subjects of his writings and re- human suffering of the time. The search include differential equations, correspondence preserved in these matrices, and semigroups. Other documents also puts into vivid relief items include several articles by other the often resentful attitude of the mathematicians on Loewner’s work, United States university establish- note cards, and a small amount of ment of that time toward refugees correspondence. Accession 2007-257 of highest creative achievement who consists of Loewner’s personal pa- were sometimes driven to accept pers, which contain correspondence

210 Notices of the AMS Volume 56, Number 2 American Mathematical Society Authors: Let the AMS Author Resource Center be your all-in-one guide for writing and publishing mathematics

General Author The Center Resources AMS Book Author includes: Resources AMS Journal Author Resources • Tools for writing mathematics, including LaTeX and TeX resources and graphics guidelines • Mathematical Reviews tools to create references and provide linking capabilities • Resources for AMS Book Authors (learn how to Author Packages prepare a proposal and how Journal author to produce and submit your packages manuscript) Monograph author Each author package packages • Specific resources for page has a simple AMS Journal Authors (find Collections and three-step process information about each proceedings volumes author to download zip files journal, explore the Author packages containing templates, Handbook, and obtain details sample files, style about copyright, permissions, files, guidelines, and manuscript tracking, and instruction manuals. more) • AMS Acquisitions Editors contact information What can the AMS Author • Answers to Frequently Asked Resource Center do for you? Questions from AMS authors and access to technical support www.ams.org/authors/ Birds and Frogs Freeman Dyson

ome mathematicians are birds, others skill as a mathematician. In his later years he hired are frogs. Birds fly high in the air and younger colleagues with the title of assistants to survey broad vistas of mathematics out do mathematical calculations for him. His way of to the far horizon. They delight in con- thinking was physical rather than mathematical. cepts that unify our thinking and bring He was supreme among physicists as a bird who togetherS diverse problems from different parts of saw further than others. I will not talk about Ein- the landscape. Frogs live in the mud below and see stein since I have nothing new to say. only the flowers that grow nearby. They delight in the details of particular objects, and they solve Francis Bacon and René Descartes problems one at a time. I happen to be a frog, but At the beginning of the seventeenth century, two many of my best friends are birds. The main theme great philosophers, Francis Bacon in England and of my talk tonight is this. Mathematics needs both René Descartes in France, proclaimed the birth of birds and frogs. Mathematics is rich and beautiful modern science. Descartes was a bird, and Bacon because birds give it broad visions and frogs give it was a frog. Each of them described his vision of intricate details. Mathematics is both great art and the future. Their visions were very different. Bacon important science, because it combines generality said, “All depends on keeping the eye steadily fixed of concepts with depth of structures. It is stupid on the facts of nature.” Descartes said, “I think, to claim that birds are better than frogs because therefore I am.” According to Bacon, scientists they see farther, or that frogs are better than birds should travel over the earth collecting facts, until because they see deeper. The world of mathemat- the accumulated facts reveal how Nature works. ics is both broad and deep, and we need birds and The scientists will then induce from the facts the frogs working together to explore it. laws that Nature obeys. According to Descartes, This talk is called the Einstein lecture, and I am scientists should stay at home and deduce the grateful to the American Mathematical Society laws of Nature by pure thought. In order to deduce for inviting me to do honor to Albert Einstein. the laws correctly, the scientists will need only Einstein was not a mathematician, but a physicist the rules of logic and knowledge of the existence who had mixed feelings about mathematics. On of God. For four hundred years since Bacon and the one hand, he had enormous respect for the Descartes led the way, science has raced ahead power of mathematics to describe the workings by following both paths simultaneously. Neither of nature, and he had an instinct for mathematical Baconian empiricism nor Cartesian dogmatism beauty which led him onto the right track to find has the power to elucidate Nature’s secrets by nature’s laws. On the other hand, he had no inter- itself, but both together have been amazingly suc- est in pure mathematics, and he had no technical cessful. For four hundred years English scientists have tended to be Baconian and French scientists Freeman Dyson is an emeritus professor in the School of Cartesian. Faraday and Darwin and Rutherford Natural Sciences, Institute for Advanced Study, Princeton, were Baconians; Pascal and Laplace and Poincaré NJ. His email address is [email protected]. were Cartesians. Science was greatly enriched by This article is a written version of his AMS Einstein Lecture, the cross-fertilization of the two contrasting cul- which was to have been given in October 2008 but which tures. Both cultures were always at work in both unfortunately had to be canceled. countries. Newton was at heart a Cartesian, using

212 NNoticesotices ofof thethe AMAMSS Volumeolume 56, Numberumber 2 pure thought as Descartes intended, and using wave mechanics in 1926. Schrödinger was a bird it to demolish the Cartesian dogma of vortices. who started from the idea of unifying mechanics Marie Curie was at heart a Baconian, boiling tons with optics. A hundred years earlier, Hamilton had of crude uranium ore to demolish the dogma of unified classical mechanics with ray optics, using the indestructibility of atoms. the same mathematics to describe optical rays In the history of twentieth century mathematics, and classical particle trajectories. Schrödinger’s there were two decisive events, one belonging to idea was to extend this unification to wave optics the Baconian tradition and the other to the Carte- and wave mechanics. Wave optics already existed, sian tradition. The first was the International Con- but wave mechanics did not. Schrödinger had to gress of Mathematicians in Paris in 1900, at which invent wave mechanics to complete the unification. Hilbert gave the keynote address, Starting from wave optics as a model, charting the course of mathematics he wrote down a differential equa- for the coming century by propound- tion for a mechanical particle, but the ing his famous list of twenty-three equation made no sense. The equation outstanding unsolved problems. Hil- looked like the equation of conduction bert himself was a bird, flying high of heat in a continuous medium. Heat over the whole territory of mathemat- conduction has no visible relevance to ics, but he addressed his problems to particle mechanics. Schrödinger’s idea the frogs who would solve them one seemed to be going nowhere. But then at a time. The second decisive event came the surprise. Schrödinger put was the formation of the Bourbaki the square root of minus one into the group of mathematical birds in France equation, and suddenly it made sense. in the 1930s, dedicated to publish- Suddenly it became a wave equation ing a series of textbooks that would instead of a heat conduction equation. establish a unifying framework for Francis Bacon And Schrödinger found to his delight all of mathematics. The Hilbert prob- that the equation has solutions cor- lems were enormously successful in responding to the quantized orbits in guiding mathematical research into the Bohr model of the atom. fruitful directions. Some of them were It turns out that the Schrödinger solved and some remain unsolved, equation describes correctly every- but almost all of them stimulated the thing we know about the behavior of growth of new ideas and new fields atoms. It is the basis of all of chem- of mathematics. The Bourbaki project istry and most of physics. And that was equally influential. It changed the square root of minus one means that style of mathematics for the next fifty nature works with complex numbers years, imposing a logical coherence and not with real numbers. This dis- that did not exist before, and moving covery came as a complete surprise, the emphasis from concrete examples to Schrödinger as well as to every- to abstract generalities. In the Bour- body else. According to Schrödinger, René Descartes baki scheme of things, mathematics is his fourteen-year-old girl friend Itha the abstract structure included in the Junger said to him at the time, “Hey, Bourbaki textbooks. What is not in the textbooks you never even thought when you began that so is not mathematics. Concrete examples, since they much sensible stuff would come out of it.” All do not appear in the textbooks, are not math- through the nineteenth century, mathematicians ematics. The Bourbaki program was the extreme from Abel to Riemann and Weierstrass had been expression of the Cartesian style. It narrowed the creating a magnificent theory of functions of scope of mathematics by excluding the beautiful complex variables. They had discovered that the flowers that Baconian travelers might collect by theory of functions became far deeper and more the wayside. powerful when it was extended from real to complex numbers. But they always thought of complex Jokes of Nature numbers as an artificial construction, invented by For me, as a Baconian, the main thing missing in human mathematicians as a useful and elegant the Bourbaki program is the element of surprise. abstraction from real life. It never entered their The Bourbaki program tried to make mathematics heads that this artificial number system that they logical. When I look at the history of mathematics, had invented was in fact the ground on which I see a succession of illogical jumps, improbable atoms move. They never imagined that nature had coincidences, jokes of nature. One of the most got there first. profound jokes of nature is the square root of Another joke of nature is the precise linearity minus one that the physicist Erwin Schrödinger of quantum mechanics, the fact that the possible put into his wave equation when he invented states of any physical object form a linear space.

February 2009 Notices of the AMS 213 Before quantum mechanics was invented, classical second commandment says: “Let your acts be di- physics was always nonlinear, and linear models rected towards a worthy goal, but do not ask if they were only approximately valid. After quantum can reach it: they are to be models and examples, mechanics, nature itself suddenly became linear. not means to an end.” Szilard practiced what he This had profound consequences for mathemat- preached. He was the first physicist to imagine ics. During the nineteenth century Sophus Lie nuclear weapons and the first to campaign ac- developed his elaborate theory of continuous tively against their use. His second commandment groups, intended to clarify the behavior of classical certainly applies here. The proof of the Riemann dynamical systems. Lie groups were then of little Hypothesis is a worthy goal, and it is not for us to interest either to mathematicians or to physicists. ask whether we can reach it. I will give you some The nonlinear theory of Lie groups was too compli- hints describing how it might be achieved. Here I cated for the mathematicians and too obscure for will be giving voice to the mathematician that I was the physicists. Lie died a disappointed man. And fifty years ago before I became a physicist. I will then, fifty years later, it turned out that nature was talk first about the Riemann Hypothesis and then precisely linear, and the theory of linear represen- about quasi-crystals. tations of Lie algebras was the natural language of There were until recently two supreme unsolved particle physics. Lie groups and Lie algebras were problems in the world of pure mathematics, the reborn as one of the central themes of twentieth proof of Fermat’s Last Theorem and the proof of century mathematics. the Riemann Hypothesis. Twelve years ago, my A third joke of nature is the existence of quasi- Princeton colleague Andrew Wiles polished off crystals. In the nineteenth century the study of Fermat’s Last Theorem, and only the Riemann Hy- crystals led to a complete enumeration of possible pothesis remains. Wiles’ proof of the Fermat Theo- discrete symmetry groups in Euclidean space. rem was not just a technical stunt. It required the Theorems were proved, establishing the fact that discovery and exploration of a new field of math- in three-dimensional space discrete symmetry ematical ideas, far wider and more consequential groups could contain only rotations of order three, than the Fermat Theorem itself. It is likely that four, or six. Then in 1984 quasi-crystals were dis- any proof of the Riemann Hypothesis will likewise covered, real solid objects growing out of liquid lead to a deeper understanding of many diverse metal alloys, showing the symmetry of the icosa- areas of mathematics and perhaps of physics too. hedral group, which includes five-fold rotations. Riemann’s zeta-function, and other zeta-func- Meanwhile, the mathematician Roger Penrose tions similar to it, appear ubiquitously in number discovered the Penrose tilings of the plane. These theory, in the theory of dynamical systems, in are arrangements of parallelograms that cover a geometry, in function theory, and in physics. The plane with pentagonal long-range order. The alloy zeta-function stands at a junction where paths lead quasi-crystals are three-dimensional analogs of in many directions. A proof of the hypothesis will the two-dimensional Penrose tilings. After these illuminate all the connections. Like every serious discoveries, mathematicians had to enlarge the student of pure mathematics, when I was young I theory of crystallographic groups to include quasi- had dreams of proving the Riemann Hypothesis. crystals. That is a major program of research which I had some vague ideas that I thought might lead is still in progress. to a proof. In recent years, after the discovery of A fourth joke of nature is a similarity in be- quasi-crystals, my ideas became a little less vague. havior between quasi-crystals and the zeros of I offer them here for the consideration of any the Riemann Zeta function. The zeros of the zeta- young mathematician who has ambitions to win function are exciting to mathematicians because a Fields Medal. they are found to lie on a straight line and nobody Quasi-crystals can exist in spaces of one, two, understands why. The statement that with trivial or three dimensions. From the point of view of exceptions they all lie on a straight line is the physics, the three-dimensional quasi-crystals are famous Riemann Hypothesis. To prove the Rie- the most interesting, since they inhabit our three- mann Hypothesis has been the dream of young dimensional world and can be studied experi- mathematicians for more than a hundred years. mentally. From the point of view of a mathemati- I am now making the outrageous suggestion that cian, one-dimensional quasi-crystals are much we might use quasi-crystals to prove the Riemann more interesting than two-dimensional or three- Hypothesis. Those of you who are mathematicians dimensional quasi-crystals because they exist in may consider the suggestion frivolous. Those who far greater variety. The mathematical definition are not mathematicians may consider it uninterest- of a quasi-crystal is as follows. A quasi-crystal ing. Nevertheless I am putting it forward for your is a distribution of discrete point masses whose serious consideration. When the physicist Leo Fourier transform is a distribution of discrete Szilard was young, he became dissatisfied with the point frequencies. Or to say it more briefly, a ten commandments of Moses and wrote a new set quasi-crystal is a pure point distribution that has of ten commandments to replace them. Szilard’s a pure point spectrum. This definition includes

214 Notices of the AMS Volume 56, Number 2 Photograph of A. Besicovitch from the AMS archives. Photo of Hermann Weyl Hermann of Photo archives. AMS the from Besicovitch A. of Photograph

as a special case the ordinary crystals, objects is a quintessentially Baconian which are periodic distributions with activity. It is an appropriate activity periodic spectra. for mathematical frogs. We shall then Excluding the ordinary crystals, find the well-known quasi-crystals quasi-crystals in three dimensions associated with PV numbers, and come in very limited variety, all of also a whole universe of other quasi- them associated with the icosahedral crystals, known and unknown. Among group. The two-dimensional quasi- the multitude of other quasi-crystals crystals are more numerous, roughly we search for one corresponding to one distinct type associated with each the Riemann zeta-function and one regular polygon in a plane. The two- corresponding to each of the other dimensional quasi-crystal with pentag- zeta-functions that resemble the Rie- onal symmetry is the famous Penrose mann zeta-function. Suppose that tiling of the plane. Finally, the one- Abram Besicovitch we find one of the quasi-crystals in dimensional quasi-crystals have a far our enumeration with properties richer structure since they are not tied that identify it with the zeros of the to any rotational symmetries. So far as Riemann zeta-function. Then we have I know, no complete enumeration of proved the Riemann Hypothesis and one-dimensional quasi-crystals exists. we can wait for the telephone call It is known that a unique quasi-crystal announcing the award of the Fields exists corresponding to every Pisot- Medal. Vijayaraghavan number or PV number. These are of course idle dreams. A PV number is a real algebraic inte- The problem of classifying one- ger, a root of a polynomial equation dimensional quasi-crystals is horren- with integer coefficients, such that all dously difficult, probably at least as the other roots have absolute value difficult as the problems that Andrew less than one, [1]. The set of all PV Wiles took seven years to explore. But numbers is infinite and has a remark- Hermann Weyl if we take a Baconian point of view, able topological structure. The set the history of mathematics is a his- of all one-dimensional quasi-crystals tory of horrendously difficult prob- has a structure at least as rich as the lems being solved by young people too ignorantpermisssion. with used Roquette, Peter of archives the tofrom Weyl H. of Photo archives. AMS from Besicovitch A. of Photograph set of all PV numbers and probably much richer. know that they were impossible. The classification We do not know for sure, but it is likely that a of quasi-crystals is a worthy goal, and might even huge universe of one-dimensional quasi-crystals turn out to be achievable. Problems of that degree not associated with PV numbers is waiting to be of difficulty will not be solved by old men like me. discovered. I leave this problem as an exercise for the young Here comes the connection of the one- frogs in the audience. dimensional quasi-crystals with the Riemann hypothesis. If the Riemann hypothesis is true, Abram Besicovitch and Hermann Weyl then the zeros of the zeta-function form a one- Let me now introduce you to some notable frogs dimensional quasi-crystal according to the defini- and birds that I knew personally. I came to Cam- tion. They constitute a distribution of point masses bridge University as a student in 1941 and had on a straight line, and their Fourier transform is the tremendous luck to be given the Russian likewise a distribution of point masses, one at each mathematician Abram Samoilovich Besicovitch of the logarithms of ordinary prime numbers and as my supervisor. Since this was in the middle prime-power numbers. My friend Andrew Odlyzko of World War Two, there were very few students has published a beautiful computer calculation of in Cambridge, and almost no graduate students. the Fourier transform of the zeta-function zeros, Although I was only seventeen years old and Besi- [6]. The calculation shows precisely the expected covitch was already a famous professor, he gave structure of the Fourier transform, with a sharp me a great deal of his time and attention, and we discontinuity at every logarithm of a prime or became life-long friends. He set the style in which prime-power number and nowhere else. I began to work and think about mathematics. He My suggestion is the following. Let us pretend gave wonderful lectures on measure-theory and that we do not know that the Riemann Hypothesis integration, smiling amiably when we laughed at is true. Let us tackle the problem from the other his glorious abuse of the English language. I re- end. Let us try to obtain a complete enumera- member only one occasion when he was annoyed tion and classification of one-dimensional quasi- by our laughter. He remained silent for a while and crystals. That is to say, we enumerate and classify then said, “Gentlemen. Fifty million English speak all point distributions that have a discrete point English you speak. Hundred and fifty million Rus- spectrum. Collecting and classifying new species of sians speak English I speak.”

February 2009 Notices of the AMS 215 Besicovitch was a frog, and he became famous into a regular and an irregular component, that when he was young by solving a problem in el- the regular component has a tangent almost ementary plane geometry known as the Kakeya everywhere, and the irregular component has a problem. The Kakeya problem was the following. projection of measure zero onto almost all direc- A line segment of length one is allowed to move tions. Roughly speaking, the regular component freely in a plane while rotating through an angle looks like a collection of continuous curves, while of 360 degrees. What is the smallest area of the the irregular component looks nothing like a con- plane that it can cover during its rotation? The tinuous curve. The existence and the properties of problem was posed by the Japanese mathematician the irregular component are connected with the Kakeya in 1917 and remained a famous unsolved Besicovitch solution of the Kakeya problem. One problem for ten years. George Birkhoff, the lead- of the problems that he gave me to work on was ing American mathematician at that time, publicly the division of measurable sets into regular and proclaimed that the Kakeya problem and the four- irregular components in spaces of higher dimen- color problem were the outstanding unsolved sions. I got nowhere with the problem, but became problems of the day. It was widely believed that permanently imprinted with the Besicovitch style. the minimum area was π/8, which is the area of a The Besicovitch style is architectural. He builds three-cusped hypocycloid. The three-cusped hypo- out of simple elements a delicate and complicated cycloid is a beautiful three-pointed curve. It is the architectural structure, usually with a hierarchical curve traced out by a point on the circumference plan, and then, when the building is finished, the of a circle with radius one-quarter, when the circle completed structure leads by simple arguments rolls around the inside of a fixed circle with radius to an unexpected conclusion. Every Besicovitch three-quarters. The line segment of length one can proof is a work of art, as carefully constructed as turn while always remaining tangent to the hypo- a Bach fugue. cycloid with its two ends also on the hypocycloid. A few years after my apprenticeship with Be- This picture of the line turning while touching the sicovitch, I came to Princeton and got to know inside of the hypocycloid at three points was so Hermann Weyl. Weyl was a prototypical bird, just elegant that most people believed it must give the as Besicovitch was a prototypical frog. I was lucky minimum area. Then Besicovitch surprised every- to overlap with Weyl for one year at the Princeton one by proving that the area covered by the line as Institute for Advanced Study before he retired it turns can be less than  for any positive . from the Institute and moved back to his old home Besicovitch had actually solved the problem in in Zürich. He liked me because during that year I 1920 before it became famous, not even knowing published papers in the Annals of Mathematics that Kakeya had proposed it. In 1920 he published about number theory and in the Physical Review the solution in Russian in the Journal of the Perm about the quantum theory of radiation. He was one Physics and Mathematics Society, a journal that of the few people alive who was at home in both was not widely read. The university of Perm, a subjects. He welcomed me to the Institute, in the city 1,100 kilometers east of Moscow, was briefly hope that I would be a bird like himself. He was dis- a refuge for many distinguished mathematicians appointed. I remained obstinately a frog. Although after the Russian revolution. They published two I poked around in a variety of mud-holes, I always volumes of their journal before it died amid the looked at them one at a time and did not look for chaos of revolution and civil war. Outside Russia connections between them. For me, number theory the journal was not only unknown but unobtain- and quantum theory were separate worlds with able. Besicovitch left Russia in 1925 and arrived at separate beauties. I did not look at them as Weyl Copenhagen, where he learned about the famous did, hoping to find clues to a grand design. Kakeya problem that he had solved five years ear- Weyl’s great contribution to the quantum theory lier. He published the solution again, this time in of radiation was his invention of gauge fields. The English in the Mathematische Zeitschrift. The Ka- idea of gauge fields had a curious history. Weyl keya problem as Kakeya proposed it was a typical invented them in 1918 as classical fields in his frog problem, a concrete problem without much unified theory of general relativity and electromag- connection with the rest of mathematics. Besico- netism, [7]. He called them “gauge fields” because vitch gave it an elegant and deep solution, which they were concerned with the non-integrability revealed a connection with general theorems about of measurements of length. His unified theory the structure of sets of points in a plane. was promptly and publicly rejected by Einstein. The Besicovitch style is seen at its finest in After this thunderbolt from on high, Weyl did his three classic papers with the title, “On the not abandon his theory but moved on to other fundamental geometric properties of linearly things. The theory had no experimental conse- measurable plane sets of points”, published in quences that could be tested. Then in 1929, after Mathematische Annalen in the years 1928, 1938, quantum mechanics had been invented by others, and 1939. In these papers he proved that every Weyl realized that his gauge fields fitted far bet- linearly measurable set in the plane is divisible ter into the quantum world than they did into the

216 Notices of the AMS Volume 56, Number 2 classical world, [8]. All astronomy, a golden that he needed to do, to age for Baconian travel- change a classical gauge ers picking up facts, for into a quantum gauge, frogs exploring small was to change real patches of the swamp numbers into complex in which we live. Dur- numbers. In quantum ing these fifty years, the mechanics, every quan- frogs accumulated a de- tum of electric charge tailed knowledge of a carries with it a com- large variety of cosmic plex wave function with structures and a large a phase, and the gauge variety of particles and field is concerned with interactions. As the the non-integrability of Chen Ning (Frank) Yuri Manin exploration of new ter- measurements of phase. Yang ritories continued, the The gauge field could universe became more then be precisely identified with the electromag- complicated. Instead of a grand design displaying netic potential, and the law of conservation of the simplicity and beauty of Weyl’s mathematics, charge became a consequence of the local phase the explorers found weird objects such as quarks invariance of the theory. and gamma-ray bursts, weird concepts such as su- Weyl died four years after he returned from persymmetry and multiple universes. Meanwhile, Princeton to Zürich, and I wrote his obituary for the mathematics was also becoming more compli- journal Nature, [3]. “Among all the mathematicians cated, as exploration continued into the phenom- who began their working lives in the twentieth ena of chaos and many other new areas opened century,” I wrote, “Hermann Weyl was the one who by electronic computers. The mathematicians made major contributions in the greatest number discovered the central mystery of computability,University. Northwestern of courtesy Manin Y. of Photo Brook. Stony SUNY of courtesy Yang F. of Photo of different fields. He alone could stand compari- the conjecture represented by the statement P is son with the last great universal mathematicians not equal to NP. The conjecture asserts that there of the nineteenth century, Hilbert and Poincaré. exist mathematical problems which can be quickly So long as he was alive, he embodied a living con- solved in individual cases but cannot be solved tact between the main lines of advance in pure by a quick algorithm applicable to all cases. The mathematics and in theoretical physics. Now he most famous example of such a problem is the is dead, the contact is broken, and our hopes of traveling salesman problem, which is to find the comprehending the physical universe by a direct shortest route for a salesman visiting a set of cit- use of creative mathematical imagination are for ies, knowing the distance between each pair. All the time being ended.” I mourned his passing, but the experts believe that the conjecture is true, and I had no desire to pursue his dream. I was happy that the traveling salesman problem is an example to see pure mathematics and physics marching of a problem that is P but not NP. But nobody has ahead in opposite directions. even a glimmer of an idea how to prove it. This is The obituary ended with a sketch of Weyl as a mystery that could not even have been formu- a human being: “Characteristic of Weyl was an lated within the nineteenth-century mathematical aesthetic sense which dominated his thinking on universe of Hermann Weyl. all subjects. He once said to me, half joking, ‘My work always tried to unite the true with the beau- Frank Yang and Yuri Manin tiful; but when I had to choose one or the other, The last fifty years have been a hard time for I usually chose the beautiful’. This remark sums birds. Even in hard times, there is work for birds up his personality perfectly. It shows his profound to do, and birds have appeared with the courage to faith in an ultimate harmony of Nature, in which tackle it. Soon after Weyl left Princeton, Frank Yang the laws should inevitably express themselves in arrived from Chicago and moved into Weyl’s old a mathematically beautiful form. It shows also house. Yang took Weyl’s place as the leading bird his recognition of human frailty, and his humor, among my generation of physicists. While Weyl which always stopped him short of being pomp- was still alive, Yang and his student Robert Mills ous. His friends in Princeton will remember him discovered the Yang-Mills theory of non-Abelian as he was when I last saw him, at the Spring Dance gauge fields, a marvelously elegant extension of of the Institute for Advanced Study last April: a Weyl’s idea of a gauge field, [11]. Weyl’s gauge field big jovial man, enjoying himself splendidly, his was a classical quantity, satisfying the commuta- cheerful frame and his light step giving no hint of tive law of multiplication. The Yang-Mills theory his sixty-nine years.” had a triplet of gauge fields which did not com- The fifty years after Weyl’s death were a golden mute. They satisfied the commutation rules of the age of experimental physics and observational three components of a quantum mechanical spin,

February 2009 Notices of the AMS 217 which are generators of the simplest non-Abelian the worlds of geometry and dynamics with his Lie algebra A2. The theory was later generalized so concept of fluxions, nowadays called calculus. In that the gauge fields could be generators of any the nineteenth century Boole linked the worlds finite-dimensional Lie algebra. With this general- of logic and algebra with his concept of symbolic ization, the Yang-Mills gauge field theory provided logic, and Riemann linked the worlds of geometry the framework for a model of all the known par- and analysis with his concept of Riemann sur- ticles and interactions, a model that is now known faces. Coordinates, fluxions, symbolic logic, and as the Standard Model of particle physics. Yang put Riemann surfaces are all metaphors, extending the finishing touch to it by showing that Einstein’s the meanings of words from familiar to unfamiliar theory of gravitation fits into the same framework, contexts. Manin sees the future of mathematics with the Christoffel three-index symbol taking the as an exploration of metaphors that are already role of gauge field, [10]. visible but not yet understood. The deepest such In an appendix to his 1918 paper, added in 1955 metaphor is the similarity in structure between for the volume of selected papers published to number theory and physics. In both fields he sees celebrate his seventieth birthday, Weyl expressed tantalizing glimpses of parallel concepts, symme- his final thoughts about gauge field theories (my tries linking the continuous with the discrete. He translation), [12]: “The strongest argument for my looks forward to a unification which he calls the theory seemed to be this, that gauge invariance quantization of mathematics. was related to conservation of electric charge in “Manin disagrees with the Baconian story, that the same way as coordinate invariance was related Hilbert set the agenda for the mathematics of the to conservation of energy and momentum.” Thirty twentieth century when he presented his famous years later Yang was in Zürich for the celebration list of twenty-three unsolved problems to the In- of Weyl’s hundredth birthday. In his speech, [12], ternational Congress of Mathematicians in Paris Yang quoted this remark as evidence of Weyl’s de- in 1900. According to Manin, Hilbert’s problems votion to the idea of gauge invariance as a unifying were a distraction from the central themes of principle for physics. Yang then went on, “Sym- mathematics. Manin sees the important advances metry, Lie groups, and gauge invariance are now in mathematics coming from programs, not from recognized, through theoretical and experimental problems. Problems are usually solved by apply- developments, to play essential roles in determining old ideas in new ways. Programs of research ing the basic forces of the physical universe. I have are the nurseries where new ideas are born. He called this the principle that symmetry dictates in- sees the Bourbaki program, rewriting the whole of teraction.” This idea, that symmetry dictates inter- mathematics in a more abstract language, as the action, is Yang’s generalization of Weyl’s remark. source of many of the new ideas of the twentieth Weyl observed that gauge invariance is intimately century. He sees the Langlands program, unifying connected with physical conservation laws. Weyl number theory with geometry, as a promising could not go further than this, because he knew source of new ideas for the twenty-first. People only the gauge invariance of commuting Abelian who solve famous unsolved problems may win big fields. Yang made the connection much stronger prizes, but people who start new programs are the by introducing non-Abelian gauge fields. With real pioneers.” non-Abelian gauge fields generating nontrivial Lie The Russian version of Mathematics as Meta- algebras, the possible forms of interaction between phor contains ten chapters that were omitted from fields become unique, so that symmetry dictates the English version. The American Mathematical interaction. This idea is Yang’s greatest contribu- Society decided that these chapters would not be tion to physics. It is the contribution of a bird, of interest to English language readers. The omis- flying high over the rain forest of little problems sions are doubly unfortunate. First, readers of the in which most of us spend our lives. English version see only a truncated view of Manin, Another bird for whom I have a deep respect who is perhaps unique among mathematicians in is the Russian mathematician Yuri Manin, who his broad range of interests extending far beyond recently published a delightful book of essays with mathematics. Second, we see a truncated view of the title Mathematics as Metaphor [5]. The book Russian culture, which is less compartmentalized was published in Moscow in Russian, and by the than English language culture, and brings math- American Mathematical Society in English. I wrote ematicians into closer contact with historians and a preface for the English version, and I give you artists and poets. here a short quote from my preface. “Mathematics as Metaphor is a good slogan for birds. It means John von Neumann that the deepest concepts in mathematics are Another important figure in twentieth century those which link one world of ideas with another. mathematics was John von Neumann. Von Neu- In the seventeenth century Descartes linked the mann was a frog, applying his prodigious tech- disparate worlds of algebra and geometry with nical skill to solve problems in many branches his concept of coordinates, and Newton linked of mathematics and physics. He began with the

218 Notices of the AMS Volume 56, Number 2 foundations of mathematics. He found the first divide the atmosphere at any moment into stable satisfactory set of axioms for set-theory, avoiding regions and unstable regions. Stable regions we the logical paradoxes that Cantor had encountered can predict. Unstable regions we can control.” Von in his attempts to deal with infinite sets and Neumann believed that any unstable region could infinite numbers. Von Neumann’s axioms were be pushed by a judiciously applied small perturba- used by his bird friend Kurt Gödel a few years later tion so that it would move in any desired direction. to prove the existence of undecidable propositions The small perturbation would be applied by a fleet in mathematics. Gödel’s theorems gave birds a new of airplanes carrying smoke generators, to absorb vision of mathematics. After Gödel, mathematics sunlight and raise or lower temperatures at places was no longer a single structure tied where the perturbation would be most together with a unique concept of effective. In particular, we could stop truth, but an archipelago of structures an incipient hurricane by identifying with diverse sets of axioms and di- the position of an instability early verse notions of truth. Gödel showed enough, and then cooling that patch that mathematics is inexhaustible. No of air before it started to rise and form matter which set of axioms is chosen a vortex. Von Neumann, speaking in as the foundation, birds can always 1950, said it would take only ten years find questions that those axioms can- to build computers powerful enough not answer. to diagnose accurately the stable and Von Neumann went on from the unstable regions of the atmosphere. foundations of mathematics to the Then, once we had accurate diagno- foundations of quantum mechanics. sis, it would take only a short time To give quantum mechanics a firm for us to have control. He expected mathematical foundation, he created John von Neumann that practical control of the weather a magnificent theory of rings of op- would be a routine operation within erators. Every observable quantity is the decade of the 1960s. represented by a linear operator, and Von Neumann, of course, was the peculiarities of quantum behav- wrong. He was wrong because he ior are faithfully represented by the did not know about chaos. We now algebra of operators. Just as Newton know that when the motion of the invented calculus to describe classi- atmosphere is locally unstable, it is cal dynamics, von Neumann invented very often chaotic. The word “chaotic” rings of operators to describe quan- means that motions that start close tum dynamics. together diverge exponentially from Von Neumann made fundamental each other as time goes on. When the contributions to several other fields, motion is chaotic, it is unpredictable, especially to game theory and to the and a small perturbation does not design of digital computers. For the Mary Cartwright move it into a stable motion that canCambridge. College, Girton Fellows, and Mistress The of courtesy Cartright Mary of Photograph last ten years of his life, he was deeply be predicted. A small perturbation involved with computers. He was so will usually move it into another cha- strongly interested in computers that he decided otic motion that is equally unpredictable. So von not only to study their design but to build one with Neumann’s strategy for controlling the weather real hardware and software and use it for doing fails. He was, after all, a great mathematician but science. I have vivid memories of the early days of a mediocre meteorologist. von Neumann’s computer project at the Institute Edward Lorenz discovered in 1963 that the so- for Advanced Study in Princeton. At that time he lutions of the equations of meteorology are often had two main scientific interests, hydrogen bombs chaotic. That was six years after von Neumann and meteorology. He used his computer during the died. Lorenz was a meteorologist and is generally night for doing hydrogen bomb calculations and regarded as the discoverer of chaos. He discovered during the day for meteorology. Most of the people the phenomena of chaos in the meteorological con- hanging around the computer building in daytime text and gave them their modern names. But in fact were meteorologists. Their leader was Jule Char- I had heard the mathematician Mary Cartwright, ney. Charney was a real meteorologist, properly who died in 1998 at the age of 97, describe the humble in dealing with the inscrutable mysteries same phenomena in a lecture in Cambridge in 1943, of the weather, and skeptical of the ability of the twenty years before Lorenz discovered them. She computer to solve the mysteries. John von Neu- called the phenomena by different names, but they mann was less humble and less skeptical. I heard were the same phenomena. She discovered them in von Neumann give a lecture about the aims of his the solutions of the van der Pol equation which de- project. He spoke, as he always did, with great con- scribe the oscillations of a nonlinear amplifier, [2]. fidence. He said, “The computer will enable us to The van der Pol equation was important in World

February 2009 Notices of the AMS 219 War II because nonlinear amplifiers fed power from the 1930s out of a drawer and dusted it off. to the transmitters in early radar systems. The The lecture was about rings of operators, a subject transmitters behaved erratically, and the Air Force that was new and fashionable in the 1930s. Noth- blamed the manufacturers for making defective ing about unsolved problems. Nothing about the amplifiers. Mary Cartwright was asked to look into future. Nothing about computers, the subject that the problem. She showed that the manufacturers we knew was dearest to von Neumann’s heart. were not to blame. She showed that the van der Pol He might at least have had something new and equation was to blame. The solutions of the van der exciting to say about computers. The audience in Pol equation have precisely the chaotic behavior the concert hall became restless. Somebody said that the Air Force was complaining about. I heard in a voice loud enough to be heard all over the all about chaos from Mary Cartwright seven years hall, “Aufgewärmte Suppe”, which is German for before I heard von Neumann talk about weather “warmed-up soup”. In 1954 the great majority of control, but I was not far-sighted enough to make mathematicians knew enough German to under- the connection. It never entered my head that the stand the joke. Von Neumann, deeply embarrassed, erratic behavior of the van der Pol equation might brought his lecture to a quick end and left the hall have something to do with meteorology. If I had without waiting for questions. been a bird rather than a frog, I would probably have seen the connection, and I might have saved Weak Chaos von Neumann a lot of trouble. If he had known If von Neumann had known about chaos when he about chaos in 1950, he would probably have spoke in Amsterdam, one of the unsolved prob- thought about it deeply, and he would have had lems that he might have talked about was weak something important to say about it in 1954. chaos. The problem of weak chaos is still unsolved Von Neumann got into trouble at the end of fifty years later. The problem is to understand his life because he was really a frog but everyone why chaotic motions often remain bounded and expected him to fly like a bird. In 1954 there was do not cause any violent instability. A good ex- an International Congress of Mathematicians in ample of weak chaos is the orbital motions of the Amsterdam. These congresses happen only once planets and satellites in the solar system. It was in four years and it is a great honor to be invited to discovered only recently that these motions are speak at the opening session. The organizers of the chaotic. This was a surprising discovery, upsetting Amsterdam congress invited von Neumann to give the traditional picture of the solar system as the the keynote speech, expecting him to repeat the act prime example of orderly stable motion. The math- that Hilbert had performed in Paris in 1900. Just as ematician Laplace two hundred years ago thought Hilbert had provided a list of unsolved problems he had proved that the solar system is stable. It to guide the development of mathematics for the now turns out that Laplace was wrong. Accurate first half of the twentieth century, von Neumann numerical integrations of the orbits show clearly was invited to do the same for the second half of that neighboring orbits diverge exponentially. It the century. The title of von Neumann’s talk was seems that chaos is almost universal in the world announced in the program of the congress. It was of classical dynamics. “Unsolved Problems in Mathematics: Address by Chaotic behavior was never suspected in the Invitation of the Organizing Committee”. After the solar system before accurate long-term integra- congress was over, the complete proceedings were tions were done, because the chaos is weak. Weak published, with the texts of all the lectures except chaos means that neighboring trajectories diverge this one. In the proceedings there is a blank page exponentially but never diverge far. The divergence with von Neumann’s name and the title of his talk. begins with exponential growth but afterwards Underneath, it says, “No manuscript of this lecture remains bounded. Because the chaos of the plan- was available.” etary motions is weak, the solar system can survive What happened? I know what happened, be- for four billion years. Although the motions are cause I was there in the audience, at 3:00 p.m. chaotic, the planets never wander far from their on Thursday, September 2, 1954, in the Concert- customary places, and the system as a whole does gebouw concert hall. The hall was packed with not fly apart. In spite of the prevalence of chaos, mathematicians, all expecting to hear a brilliant the Laplacian view of the solar system as a perfect lecture worthy of such a historic occasion. The piece of clockwork is not far from the truth. lecture was a huge disappointment. Von Neumann We see the same phenomena of weak chaos in had probably agreed several years earlier to give the domain of meteorology. Although the weather a lecture about unsolved problems and had then in New Jersey is painfully chaotic, the chaos has forgotten about it. Being busy with many other firm limits. Summers and winters are unpredict- things, he had neglected to prepare the lecture. ably mild or severe, but we can reliably predict Then, at the last moment, when he remembered that the temperature will never rise to 45 degrees that he had to travel to Amsterdam and say some- Celsius or fall to minus 30, extremes that are thing about mathematics, he pulled an old lecture often exceeded in India or in Minnesota. There

220 Notices of the AMS Volume 56, Number 2 is no conservation law of physics that forbids solve old problems that were previously unsolvable. temperatures from rising as high in New Jersey Second, the string theorists think of themselves as in India, or from falling as low in New Jersey as physicists rather than mathematicians. They as in Minnesota. The weakness of chaos has been believe that their theory describes something real essential to the long-term survival of life on this in the physical world. And third, there is not yet planet. Weak chaos gives us a challenging variety any proof that the theory is relevant to physics. of weather while protecting us from fluctuations The theory is not yet testable by experiment. The so severe as to endanger our existence. Chaos theory remains in a world of its own, detached remains mercifully weak for reasons that we do from the rest of physics. String theorists make not understand. That is another unsolved problem strenuous efforts to deduce consequences of the for young frogs in the audience to take home. I theory that might be testable in the real world, so challenge you to understand the reasons why the far without success. chaos observed in a great diversity of dynamical My colleagues Ed Witten and Juan Maldacena systems is generally weak. and others who created string theory are birds, The subject of chaos is characterized by an flying high and seeing grand visions of distant abundance of quantitative data, an unending sup- ranges of mountains. The thousands of hum- ply of beautiful pictures, and a shortage of rigor- bler practitioners of string theory in universities ous theorems. Rigorous theorems are the best way around the world are frogs, exploring fine details to give a subject intellectual depth and precision. of the mathematical structures that birds first Until you can prove rigorous theorems, you do not saw on the horizon. My anxieties about string fully understand the meaning of your concepts. theory are sociological rather than scientific. It is In the field of chaos I know only one rigorous a glorious thing to be one of the first thousand theorem, proved by Tien-Yien Li and Jim Yorke in string theorists, discovering new connections and 1975 and published in a short paper with the title, pioneering new methods. It is not so glorious to “Period Three Implies Chaos”, [4]. The Li-Yorke be one of the second thousand or one of the tenth paper is one of the immortal gems in the literature thousand. There are now about ten thousand of mathematics. Their theorem concerns nonlinear string theorists scattered around the world. This maps of an interval onto itself. The successive posi- is a dangerous situation for the tenth thousand tions of a point when the mapping is repeated can and perhaps also for the second thousand. It may be considered as the orbit of a classical particle. happen unpredictably that the fashion changes An orbit has period N if the point returns to its and string theory becomes unfashionable. Then it original position after N mappings. An orbit is could happen that nine thousand string theorists defined to be chaotic, in this context, if it diverges lose their jobs. They have been trained in a narrow from all periodic orbits. The theorem says that if a specialty, and they may be unemployable in other single orbit with period three exists, then chaotic fields of science. orbits also exist. The proof is simple and short. To Why are so many young people attracted to my mind, this theorem and its proof throw more string theory? The attraction is partly intellectual. light than a thousand beautiful pictures on the String theory is daring and mathematically elegant. basic nature of chaos. The theorem explains why But the attraction is also sociological. String theory chaos is prevalent in the world. It does not explain is attractive because it offers jobs. And why are why chaos is so often weak. That remains a task so many jobs offered in string theory? Because for the future. I believe that weak chaos will not string theory is cheap. If you are the chairperson be understood in a fundamental way until we can of a physics department in a remote place without prove rigorous theorems about it. much money, you cannot afford to build a modern laboratory to do experimental physics, but you can String Theorists afford to hire a couple of string theorists. So you I would like to say a few words about string theory. offer a couple of jobs in string theory, and you Few words, because I know very little about string have a modern physics department. The tempta- theory. I never took the trouble to learn the subject tions are strong for the chairperson to offer such or to work on it myself. But when I am at home at the jobs and for the young people to accept them. Institute for Advanced Study in Princeton, I am sur- This is a hazardous situation for the young people rounded by string theorists, and I sometimes listen and also for the future of science. I am not say- to their conversations. Occasionally I understand a ing that we should discourage young people from little of what they are saying. Three things are clear. working in string theory if they find it exciting. I First, what they are doing is first-rate mathemat- am saying that we should offer them alternatives, ics. The leading pure mathematicians, people like so that they are not pushed into string theory by Michael Atiyah and Isadore Singer, love it. It has economic necessity. opened up a whole new branch of mathematics, Finally, I give you my own guess for the future with new ideas and new problems. Most remark- of string theory. My guess is probably wrong. I ably, it gave the mathematicians new methods to have no illusion that I can predict the future. I tell

February 2009 Notices of the AMS 221 you my guess, just to give you something to think Jung, is a mental image rooted in a collective un- about. I consider it unlikely that string theory will conscious that we all share. The intense emotions turn out to be either totally successful or totally that archetypes carry with them are relics of lost useless. By totally successful I mean that it is a memories of collective joy and suffering. Manin is complete theory of physics, explaining all the de- saying that we do not need to accept Jung’s theory tails of particles and their interactions. By totally as true in order to find it illuminating. useless I mean that it remains a beautiful piece of More than thirty years ago, the singer Monique pure mathematics. My guess is that string theory Morelli made a recording of songs with words by will end somewhere between complete success Pierre MacOrlan. One of the songs is La Ville Morte, and failure. I guess that it will be like the theory the dead city, with a haunting melody tuned to of Lie groups, which Sophus Lie created in the Morelli’s deep contralto, with an accordion singing nineteenth century as a mathematical framework counterpoint to the voice, and with verbal images for classical physics. So long as physics remained of extraordinary intensity. Printed on the page, the classical, Lie groups remained a failure. They were words are nothing special: a solution looking for a problem. But then, fifty “En pénétrant dans la ville morte, years later, the quantum revolution transformed Je tenait Margot par le main… physics, and Lie algebras found their proper place. Nous marchions de la nécropole, They became the key to understanding the central Les pieds brisés et sans parole, role of symmetries in the quantum world. I expect Devant ces portes sans cadole, that fifty or a hundred years from now another Devant ces trous indéfinis, revolution in physics will happen, introducing new Devant ces portes sans parole concepts of which we now have no inkling, and the Et ces poubelles pleines de cris”. new concepts will give string theory a new mean- “As we entered the dead city, I held Margot by ing. After that, string theory will suddenly find the hand…We walked from the graveyard on our its proper place in the universe, making testable bruised feet, without a word, passing by these statements about the real world. I warn you that doors without locks, these vaguely glimpsed holes, this guess about the future is probably wrong. It these doors without a word, these garbage cans has the virtue of being falsifiable, which accord- full of screams.” ing to Karl Popper is the hallmark of a scientific I can never listen to that song without a dispro- statement. It may be demolished tomorrow by portionate intensity of feeling. I often ask myself some discovery coming out of the Large Hadron why the simple words of the song seem to resonate Collider in Geneva. with some deep level of unconscious memory, as Manin Again if the souls of the departed are speaking through Morelli’s music. And now unexpectedly in Manin’s To end this talk, I come back to Yuri Manin and book I find an answer to my question. In his chap- his book Mathematics as Metaphor. The book ter, “The Empty City Archetype”, Manin describes is mainly about mathematics. It may come as a how the archetype of the dead city appears again surprise to Western readers that he writes with and again in the creations of architecture, litera- equal eloquence about other subjects such as the ture, art and film, from ancient to modern times, collective unconscious, the origin of human lan- ever since human beings began to congregate in guage, the psychology of autism, and the role of cities, ever since other human beings began to the trickster in the mythology of many cultures. congregate in armies to ravage and destroy them. To his compatriots in Russia, such many-sided The character who speaks to us in MacOrlan’s song interests and expertise would come as no surprise. is an old soldier who has long ago been part of an Russian intellectuals maintain the proud tradition army of occupation. After he has walked with his of the old Russian intelligentsia, with scientists wife through the dust and ashes of the dead city, and poets and artists and musicians belonging to he hears once more: a single community. They are still today, as we see them in the plays of Chekhov, a group of idealists “Chansons de charme d’un clairon bound together by their alienation from a super- Qui fleurissait une heure lointaine stitious society and a capricious government. In Dans un rêve de garnison”. Russia, mathematicians and composers and film- “The magic calls of a bugle that came to life for producers talk to one another, walk together in the an hour in an old soldier’s dream”. snow on winter nights, sit together over a bottle of The words of MacOrlan and the voice of Mo- wine, and share each others’ thoughts. relli seem to be bringing to life a dream from our Manin is a bird whose vision extends far be- collective unconscious, a dream of an old soldier yond the territory of mathematics into the wider wandering through a dead city. The concept of the landscape of human culture. One of his hobbies collective unconscious may be as mythical as the is the theory of archetypes invented by the Swiss concept of the dead city. Manin’s chapter describes psychologist Carl Jung. An archetype, according to the subtle light that these two possibly mythical

222 Notices of the AMS Volume 56, Number 2 concepts throw upon each other. He describes the collective unconscious as an irrational force that powerfully pulls us toward death and destruction. The archetype of the dead city is a distillation of the agonies of hundreds of real cities that have been destroyed since cities and marauding armies 0ROFESSOROF-ATHEMATICS were invented. Our only way of escape from the /PERATIONS2ESEARCH insanity of the collective unconscious is a collec- 4HE $EPARTMENT OF -ATHEMATICS WWWMATHETHZCH AT %4( :~RICH tive consciousness of sanity, based upon hope INVITESAPPLICATIONSFORAFACULTYPOSITIONINMATHEMATICSOFOPERATIONS and reason. The great task that faces our contem- RESEARCH4HEDUTIESOFTHEFUTUREPROFESSOR WHOWILLBEAMEMBEROF THE$EPARTMENTOF-ATHEMATICS INCLUDETEACHINGANDRESEARCHINTHE porary civilization is to create such a collective MATHEMATICS OF OPERATIONS RESEARCH AND RELATED AREAS 4HE PERSPEC consciousness. TIVEOFTHEPOSITIONINCLUDESTHEHEADINGOFTHE)NSTITUTEFOR/PERATIONS 2ESEARCHAT%4(:URICH References 7EARESEEKINGCANDIDATESWITHANINTERNATIONALLYRECOGNIZEDRESEARCH RECORDINMATHEMATICSRELATEDTOOPERATIONSRESEARCHANDWITHPROVEN [1] M. J. Bertin et al., Pisot and Salem Numbers, ABILITYTODIRECTRESEARCHOFHIGHQUALITY%XPERTISEANDASTRONGBACK Birkhäuser Verlag, Basel, 1992. GROUNDINOPTIMIZATIONANDORCOMPUTATIONWILLBEESPECIALLYAPPRECI [2] M. L. Cartwright and J. E. Littlewood, On non- ATED 7ILLINGNESS TO TEACH AT ALL UNIVERSITY LEVELS AND TO COLLABORATE WITHCOLLEAGUESFROMENGINEERINGANDINDUSTRYISEXPECTED linear differential equations of the second order, I, Jour. London Math. Soc. 20 (1945), 180–189. 4OGETHERWITHTHECOLLEAGUESFROMTHEDEPARTMENT THENEWPROFES SOR WILL BE RESPONSIBLE FOR UNDERGRADUATE COURSES IN MATHEMATICS [3] Freeman Dyson, Prof. Hermann Weyl, For.Mem.R.S., AT%4(:URICHFORSTUDENTSOFMATHEMATICS ENGINEERINGANDNATURAL Nature 177 (1956), 457–458. SCIENCES ANDFORGRADUATECOURSESINTHEPROGRAMMES-3CIN!PPLIED [4] Tien-Yien Li and James A. Yorke, Period three implies -ATHEMATICS -3CIN#OMPUTATIONAL3CIENCEAND%NGINEERING -3CIN chaos, Amer. Math. Monthly 82 (1975), 985–992. 3TATISTICS AND-3CIN1UANTITATIVE&INANCEJOINTDEGREEWITHTHE5NI VERSITYOF:~RICH 4HESUCCESSFULCANDIDATEWILLBEEXPECTEDTOTEACH [5] Yuri I. Manin, Mathematics as Metaphor: Selected UNDERGRADUATELEVELCOURSES'ERMANOR%NGLISH ANDGRADUATELEVEL Essays, American Mathematical Society, Providence, COURSES%NGLISH Rhode Island, 2007. [The Russian version is: Manin, 0LEASESUBMITYOURAPPLICATIONWITHACURRICULUMVITAEANDLISTOFPUB Yu. I., Matematika kak Metafora, Moskva, Izdatyelstvo LICATIONSTOTHE0RESIDENTOF%4(:URICH 0ROF$R2ALPH%ICHLER 2AE MTsNMO, 2008.] MISTRASSE :URICH 3WITZERLAND NOLATERTHAN-ARCH 7ITHAVIEWTOWARDINCREASINGTHENUMBEROFFEMALEPROFESSORS %4( [6] Andrew M. Odlyzko, Primes, quantum chaos and :URICHSPECIFICALLYENCOURAGESFEMALECANDIDATESTOAPPLY computers, in Number Theory, Proceedings of a Sym- posium, National Research Council, Washington DC, 1990, pp. 35–46. [7] Hermann Weyl, Gravitation und elektrizität, Sitz. König. Preuss. Akad. Wiss. 26 (1918), 465–480. [8] ——— , Elektron und gravitation, Zeits. Phys. 56 (1929), 350–352. New Directions Short Course [9] ——— , Selecta, Birkhäuser Verlag, Basel, 1956, Applied Algebraic Topology p. 192. June 15-26, 2009 [10] Chen Ning Yang, Integral formalism for gauge fields, Phys. Rev. Letters 33 (1974), 445–447. Instructors: [11] Chen Ning Yang and Robert L. Mills, Conservation Gunnar Carlsson (Stanford University) of isotopic spin and isotopic gauge invariance, Phys. Robert Ghrist (University of Pennsylvania) Rev. 96 (1954), 191–195. From June 15-26, 2009 the IMA will host an intensive [12] ——— , Hermann Weyl’s contribution to physics, in Hermann Weyl, 1885–1985, (K. Chandrasekharan, ed.), short course designed to efficiently provide researchers Springer-Verlag, Berlin, 1986, p. 19. in the mathematical sciences and related disciplines the basic knowledge prerequisite to undertake research in applied algebraic topology. The course will be taught by Gunnar Carlsson (Department of Mathematics, Stanford University) and Robert Ghrist (Department of Electrical and Systems Engineering, Department of Mathematics, University of Pennsylvania). The primary audience for the course is mathematics faculty. No prior background in applied algebraic topology is expected. Participants will receive full travel and lodging support during the workshop. For more information and to apply: www.ima.umn.edu/2008-2009/ND6.15-26.09 Application deadline: April 1, 2009

The IMA is an NSF funded institute

February 2009 Notices of the AMS 223 Mathematics Research Communities Program Kicks Off Allyn Jackson

“Talking to so many other young mathematicians with my same interests was very inspiring.” “I felt that this conference is unique in how it allowed me to make connections with others in my field that could easily blossom into working relationships.” “The conference was wonderful…Many collaborations will come out of it. This is invaluable for lectures, most of the activities are in the hands of young mathematicians like me. the participants, who lecture to each other about Also, it was a lot of fun in a beauti- their work and hold informal sessions for exchang- ful place.” ing ideas. Included are professional development sessions covering such topics as how to write a These are typical comments from research grant and job search tips. Participants participants in Mathematics Re- also take responsibility for organizing special search Communities (MRC), an sessions at the Joint Mathematics Meetings, they innovative program started by the AMS to help young mathema- stay in touch during the academic year through ticians create networks of peers electronic discussion networks by research topic, who are interested in similar areas and they are provided with ongoing mentoring by of research. With support from the conference organizers. The AMS is also carry- the National Science Foundation, ing out a longitudinal study of the careers of the MRC got off the ground in summer MRC participants. (The quotations in this article 2008 with three 1-week confer- are taken from participant responses to questions ences held in Snowbird, Utah. The in an online survey.) program also provides means to The largest of the three 2008 conferences fo- keep the participants connected cused on low-dimensional topology and Teichmül- during the 2008–2009 academic ler theory and had about forty participants. The year. A new set of conferences will mornings were devoted to expository talks and the be held in summer 2009. afternoons to short presentations by the partici- The MRC conferences have a pants, each of whom gave a talk on their research unique structure: They are orga- interests. While the nature and quality of the talks nized by a small number of senior was not uniform, they helped participants to find mathematicians, but all of the others with similar interests. “I really appreciated participants are graduate students that the conference was meant as a stepping-stone or postdocs. While the organizers for us to collaborate with others,” said one partici- are there to keep everything run- pant. “The short talks…helped us find each other.” ning smoothly and to give some Another participant commented that the highlight

224 Notices of the AMS Volume 56, Number 2 of the conference came when others sought him out to ask him about his talk. There were also informal sessions that drew many questions and much discussion about what the major open questions are in the area. “The program gave the participants exposure to a nice mixture of elementary topics and current research,” one participant said. “I wouldn’t change anything.” The two other conferences were smaller, with about twenty participants apiece. The first, which focused on computational algebra and convexity, had two main themes: studying a 2006 paper that contains new ideas and technical tools that would be useful for the students to master, and exploring the use of computational algebra software for computing primary decomposition. The participants “I came not knowing anyone, broke up into working groups centered on the and left with a whole new com- two themes, and each group made a presentation munity of researchers.” at the end of the conference. “I appreciated…the A new crop of MRC partici- chance to wrap pants will join in four confer- it all up into a ences to be held in summer ‘final presenta- 2009, again in Snowbird. The tion’ of what we dates and topics of the confer- had learned,” one ences are: June 13–19, 2009, participant com- Mathematical Challenges of mented. “That re- Relativity; June 20–26, 2009, ally helped crys- Inverse Problems; June 27– tallize how much July 3, 2009, Modern Markov progress we had Chains and Their Statistical made in a week.” Applications; and June 27– The format of the July 3, 2009, Harmonic Analy- MRC conferences is very flexible, and early on sis. For further information the organizers realized that having some evening about applying, see “Mathemat- “basic notions” talks would be helpful. These talks ics Opportunities” in this issue were held from 9:00 p.m. to 10:00 p.m. after a long of the Notices or consult the day, but this did not dampen participants’ enthu- webpage http://www.ams. siasm. “We could ask the dumbest questions and org/amsmtgs/mrc-09.html. get good answers without fear of looking dumb,” The application deadline one participant commented. “It was a great learn- is March 2, 2009, for ing environment!” participation in the sum- The third conference was on scientific comput- mer 2009 conferences. In ing and advanced computation. “Overall the pro- addition, organizers are gram was one of the best and richest experiences I sought for MRC confer- have had,” one of the participants commented. The ences in summer 2010; primary topics discussed were new programming a call for organizers ap- languages for scientific computing, parallel com- peared in the January puting, and multiscale analysis. There were several 2009 issue of the Notices, talks by senior researchers, after which the partici- page 87, and is available pants carried out group work. One novel feature of on the Web at http:// this conference was an exercise in grant writing. www.ams.org/amsmtgs/ Participants broke up into groups and selected a mrc-proposals.html. project about which to write proposals and chose —Allyn Jackson one group member to be the lead principal inves- tigator. Then each member of the group helped write a “letter of intent” and presentation slides. Photographs courtesy of On the last day of the MRC, groups presented their David Eisenbud and Ellen proposals to a panel of senior researchers. The Maycock. intensive group work spurred rich interactions among the participants. “The highlight for me was definitely the people,” one participant remarked.

February 2009 Notices of the AMS 225 The Strong Free Will Theorem John H. Conway and Simon Kochen

he two theories that revolutionized fortunate because these theoretical notions have physics in the twentieth century, rela- led to much confusion. For instance, it is often said tivity and quantum mechanics, are full that the probabilities of events at one location can of predictions that defy common sense. be instantaneously changed by happenings at an- Recently, we used three such para- other space-like separated location, but whether Tdoxical ideas to prove “The Free Will Theorem” that is true or even meaningful is irrelevant to (strengthened here), which is the culmination of our proof, which never refers to the notion of a series of theorems about quantum mechanics probability. that began in the 1960s. It asserts, roughly, that if For readers of the original version [1] of our indeed we humans have free will, then elementary theorem, we note that we have strengthened it particles already have their own small share of by replacing the axiom FIN together with the as- this valuable commodity. More precisely, if the sumption of the experimenters’ free choice and experimenter can freely choose the directions temporal causality by a single weaker axiom MIN. in which to orient his apparatus in a certain The earlier axiom FIN of [1], that there is a finite measurement, then the particle’s response (to upper bound to the speed with which informa- be pedantic—the universe’s response near the tion can be transmitted, has been objected to by particle) is not determined by the entire previous history of the universe. several authors. Bassi and Ghirardi asked in [3]: Our argument combines the well-known conse- what precisely is “information”, and do the “hits” quence of relativity theory, that the time order of and “flashes” of GRW theories (discussed in the space-like separated events is not absolute, with Appendix) count as information? Why cannot hits the EPR paradox discovered by Einstein, Podolsky, be transmitted instantaneously, but not count as and Rosen in 1935, and the Kochen-Specker Para- signals? These objections miss the point. The only dox of 1967 (See [2].) We follow Bohm in using a information to which we applied FIN is the choice spin version of EPR and Peres in using his set of 33 made by the experimenter and the response of directions, rather than the original configuration the particle, as signaled by the orientation of the used by Kochen and Specker. More contentiously, apparatus and the spot on the screen. The speed the argument also involves the notion of free will, of transmission of any other information is irrel- but we postpone further discussion of this to the evant to our argument. The replacement of FIN last section of the article. by MIN has made this fact explicit. The theorem Note that our proof does not mention “probabil- has been further strengthened by allowing the ities” or the “states” that determine them, which is particles’ responses to depend on past half-spaces rather than just the past light cones of [1]. John H. Conway is professor of mathematics at Princeton University. His email address is [email protected]. Simon Kochen is professor of mathematics at Prince- The Axioms ton University. His email address is kochen@math. We now present and discuss the three axioms on princeton.edu. which the theorem rests.

226 Notices of the AMS Volume 56, Number 2 Figure 1. The three colored cubes in Figure 1a are obtained by rotating the white cube through 45◦ about its coordinate axes. The 33 directions are the symmetry axes of the colored cubes and pass through the spots in Figure 1a. Figure 1b shows where these directions meet the white cube.

(i) The SPIN Axiom and the Kochen-Specker Para- Proof. We shall call a node even or odd according dox as the putative 101 function is supposed to take Richard Feynman once said that “If someone the value 0 or 1 at it, and we progressively assign tells you they understand quantum mechanics, even or odd numbers to the nodes in Figure 1b as then all you’ve learned is that you’ve met a liar.” we establish the contradiction. Our first axiom initially seems easy to understand, We shall use some easily justified orthogonal- but beware—Feynman’s remark applies! The ax- ities—for instance the coordinate triple rotates to iom involves the operation called “measuring the the triple (2, 3, −3) that starts our proof, which squared spin of a spin 1 particle”, which always in turn rotates (about −1) to the triples (8, −7, 9) produces the result 0 or 1. and (−8, 7, −9) that finish it. SPIN Axiom: Measurements of the squared (com- Without loss of generality nodes 1 and −1 are ponents of) spin of a spin 1 particle in three orthog- odd and node 2 even, forcing 3 and −3 to be odd. onal directions always give the answers 1, 0, 1 in Now nodes 4 and -x form a triple with 3, so one of some order. them (without loss of generality 4) is even. In view − Quantum mechanics predicts this axiom since of the reflection that interchanges 4 and x while for a spin 1 particle the squared spin operators fixing 4 and -x, we can without loss of generality − s2, s2, s2 commute and have sum 2. suppose that 4 is also even. x y z There is a 90◦ rotation about 1 that moves 7, 5, 9 This “101 property” is paradoxical because it to 4, 6, x, showing that 5 is orthogonal to 4, while already implies that the quantity that is suppos- 1, 5, 6 is a triple, and also that 6 is orthogonal to edly being measured cannot in fact exist before both 7 and 9. Thus 5 is odd, 6 even, and 7, 9 odd. its “measurement”. For otherwise there would be A similar argument applies to nodes −5, −6, −7, a function defined on the sphere of possible di- −9. rections taking each orthogonal triple to 1, 0, 1 in Finally, 8 forms a triple with −7 and 9, as does some order. It follows from this that it takes the −8 with 7 and −9. So both these nodes must same value on pairs of opposite directions, and be even, and since they are orthogonal, this is a never takes two orthogonal directions to 0. contradiction that completes the proof. We call a function defined on a set of direc- Despite the Kochen-Specker paradox, no physi- tions that has all three of these properties a “101 cist would question the truth of our SPIN axiom, function” for that set. But unfortunately we have: since it follows from quantum mechanics, which The Kochen-Specker Paradox: There does not is one of the most strongly substantiated scien- exist a 101 function for the 33 pairs of directions of tific theories of all time. However, it is important Figure 1 (the Peres configuration). to realize that we do not in fact suppose all of

February 2009 Notices of the AMS 227 quantum mechanics, but only two of its testable the choice an experimenter makes is not a func- consequences, namely this axiom SPIN and the tion of the past. We explicitly use only some very axiom TWIN of the next section. special cases of these assumptions in justifying It is true that these two axioms deal only with our final axiom. idealized forms of experimentally verifiable pre- The MIN Axiom: Assume that the experiments dictions, since they refer to exact orthogonal and performed by A and B are space-like separated. parallel directions in space. However, as we have Then experimenter B can freely choose any one of shown in [1], the theorem is robust, in that approx- the 33 particular directions w, and a’s response imate forms of these axioms still lead to a similar is independent of this choice. Similarly and inde- conclusion. At the same time, this shows that any pendently, A can freely choose any one of the 40 more accurate modifications of special relativity triples x, y, z, and b’s response is independent of (such as general relativity) and of quantum theory that choice. will not affect the conclusions of the theorem. It is the experimenters’ free will that allows the free and independent choices of x, y, z, and w. But (ii) The TWIN Axiom and the EPR Paradox in one inertial frame—call it the “A-first” frame— One of the most curious facts about quantum B’s experiment will only happen some time later mechanics was pointed out by Einstein, Podolsky, than A’s, and so a’s response cannot, by temporal and Rosen in 1935. This says that even though the causality, be affected by B’s later choice of w. In a results of certain remotely separated observations B-first frame, the situation is reversed, justifying cannot be individually predicted ahead of time, the final part of MIN. (We shall discuss the mean- they can be correlated. ing of the term “independent” more fully in the In particular, it is possible to produce a pair of Appendix.) “twinned” spin 1 particles (by putting them into the “singleton state” of total spin zero) that will The (Strong) Free Will Theorem give the same answers to the above squared spin Our theorem is a strengthened form of the original measurements in parallel directions. Our “TWIN” version of [1]. Before stating it, we make our terms axiom is part of this assertion. more precise. We use the words “properties”, The TWIN Axiom: For twinned spin 1 particles, “events”, and “information” almost interchange- suppose experimenter A performs a triple exper- ably: whether an event has happened is a property, iment of measuring the squared spin component and whether a property obtains can be coded by of particle a in three orthogonal directions x, y, z, an information-bit. The exact general meaning of while experimenter B measures the twinned par- these terms, which may vary with some theory ticle b in one direction, w. Then if w happens to that may be considered, is not important, since we be in the same direction as one of x, y, z, experi- only use them in the specific context of our three menter B’s measurement will necessarily yield the axioms. same answer as the corresponding measurement To say that A’s choice of x, y, z is free means by A. more precisely that it is not determined by (i.e., In fact we will restrict w to be one of the 33 di- is not a function of) what has happened at earlier rections in the Peres configuration of the previous times (in any inertial frame). Our theorem is the section, and x, y, z to be one of 40 particular or- surprising consequence that particle a’s response thogonal triples, namely the 16 such triples of that must be free in exactly the same sense, that it is configuration and the 24 further triples obtained not a function of what has happened earlier (with by completing its remaining orthogonal pairs. respect to any inertial frame). (iii) The MIN Axiom, Relativity, and Free Will The Free Will Theorem. The axioms SPIN, TWIN One of the paradoxes introduced by relativity and MIN imply that the response of a spin 1 parti- was the fact that temporal order depends on the cle to a triple experiment is free—that is to say, is choice of inertial frame. If two events are space- not a function of properties of that part of the uni- like separated, then they will appear in one time verse that is earlier than this response with respect order with respect to some inertial frames, but to any given inertial frame. in the reverse order with respect to others. The Proof. We suppose to the contrary—this is the two events we use will be the above twinned spin “functional hypothesis” of [1]—that particle a’s measurements. response (i, j, k) to the triple experiment with It is usual tacitly to assume the temporal causal- directions x, y, z is given by a function of proper- ity principle that the future cannot alter the past. ties α, . . . that are earlier than this response with Its relativistic form is that an event cannot be influ- respect to some inertial frame F. We write this as enced by what happens later in any given inertial F = frame. Another customarily tacit assumption is θa (α) one of (0, 1, 1), (1, 0, 1), (1, 1, 0) that experimenters are free to choose between (in which only a typical one of the properties α is possible experiments. To be precise, we mean that indicated).

228 Notices of the AMS Volume 56, Number 2 Similarly we suppose that b’s response 0 or 1 We now define for the direction w is given by a function G = G θ0 (w) θb (x, y, z, w; β0), G = θb (β) one of 0 or 1 noting that since by MIN the response of b cannot G vary with x, y, z, θ0 is a function just of w. of properties β, . . . that are earlier with respect to ′ a possibly different inertial frame G. Similarly there is a value α0 of α for which the F function (i) If either one of these functions, say θa , is F = F influenced by some information that is free in the θ1 (x, y, z) θa (x, y, z, w; α0) above sense (i.e., not a function of A’s choice of is defined for all 40 triples x, y, z, and it is al- directions and events F-earlier than that choice), so independent of w, which argument we have then there must be an an earliest (“infimum”) therefore omitted. F-time t0 after which all such information is avail- But now by TWIN we have the equation able to a. Since the non-free information is also F = G G G θ1 (x, y, z) (θ0 (x), θ0 (y), θ0 (z)) . available at t0, all these information bits, free and non-free, must have a value 0 or 1 to enter as However, since by SPIN the value of the left-hand F arguments in the function θa . So we regard a’s side is one of (0, 1, 1), (1, 0, 1), (1, 1, 0), this shows G response as having started at t0. that θ0 is a 101 function, which the Kochen- If indeed, there is any free bit that influences Specker paradox shows does not exist. This com- a, the universe has by definition taken a free pletes the proof. decision near a by time t0, and we remove the pedantry by ascribing this decision to particle a. Locating the Response (This is discussed more fully in the section “Free We now provide a fuller discussion of some delicate Will Versus Determinism”.) points. (ii) From now on we can suppose that no such (i) Since the observed spot on the screen is the new information bits influence the particles’ re- result of a cascade of slightly earlier events, it sponses, and therefore that α and β are functions is hard to define just when “the response” really of the respective experimenters’ choices and of starts. We shall now explain why one can regard events earlier than those choices. a’s response (say) as having already started at any Now an α can be expected to vary with x, y, z time after A’s choice when all the free information and may or may not vary with w. However, whether bits that influence it have become available to a. the function varies with them or not, we can intro- Let N(a) and N(b) be convex regions of space- duce all of x, y, z, w as new arguments and rewrite time that are just big enough to be “neighborhoods F θa as a new function (which for convenience we of the respective experiments”, by which we mean give the same name) that they contain the chosen settings of the ap- ′ paratus and the appropriate particle’s responses. θF (x, y, z, w; α ) (⋆) a Our proof has shown that if the backward half- ′ of x, y, z, w and properties α independent of space t < tF determined by a given F-time tF is x, y, z, w. disjoint from N(a), then the available informa- To see this, replace any α that does depend tion it contains is not enough to determine a’s on x, y, z, w by the constant values α1, . . . , α1320 it response. On the other hand, if each of the two takes for the 40 × 33 = 1320 particular quadru- such half-spaces contains the respective neigh- ples x, y, z, w we shall use. Alternatively, if each borhood, then of course they already contain the α is some function α(x, y, z, w) of x, y, z, w, we responses. By varying F and G, this suffices to lo- may substitute these functions in (⋆) to obtain cate the free decisions to the two neighborhoods, information bits independent of x, y, z, w. which justifies our ascribing it to the particles G Similarly, we can rewrite θb as a function themselves. θG(x, y, z, w; β′) (ii) We remark that not all the information in the b G-backward half-space (say) need be available to ′ G of x, y, z, w and properties β independent of b, because MIN prevents particle b’s function θb x, y, z, w. from using experimenter A’s choice of directions Now for the particular choice of w that B will x, y, z. The underlying reason is of course, that rel- ′ make, there is a value β0 for β for which ativity allows us to view the situation from a B-first frame, in which A’s choice is made only later than θG(x, y, z, w; β ) b 0 b’s response, so that A is still free to choose an is defined. By the above independence of β′ from arbitrary one of the 40 triples. However, this is our G w, the function θb (x, y, z, w; β0) is defined with only use of relativistic invariance—the argument the same value β0 for all 33 values of w. (The fact actually allows any information that does not re- that MIN allows B to freely vary his choice of w veal A’s choice to be transmitted superluminally, makes this intuitively clear.) or even backwards in time.

February 2009 Notices of the AMS 229 (iii) Although we’ve precluded the possibility Historically, this kind of correlation was a great G that θb can vary with A’s choice of directions, it is surprise, which many authors have tried to ex- conceivable that it might nevertheless varywith a’s plain away by saying that one particle influences G (future!) response. However, θb cannot be affected the other. However, as we argue in detail in [1], by a’s response to an unknown triple chosen by the correlation is relativistically invariant, unlike A, since the same information is conveyed by the any such explanation. Our attitude is different: responses (0, 1, 1), to (x, y, z), (1, 0, 1) to (z, x, y), following Newton’s famous dictum “Hypotheses F non fingo”, we attempt no explanation, but accept and (1, 1, 0) to (y, z, x). For a similar reason θa cannot use b’s response, since B’s experiment the correlation as a fact of life. might be to investigate some orthogonal triple Some believe that the alternative to determin- u, v, w and discard the responses corresponding ism is randomness, and go on to say that “allowing to u and v. randomness into the world does not really help in understanding free will.” However, this objec- (iv) It might be objected that free will itself tion does not apply to the free responses of the might in some sense be frame-dependent. Howev- particles that we have described. It may well be er, the only instance used in our proof is the choice true that classically stochastic processes such as of directions, which, since it becomes manifest in tossing a (true) coin do not help in explaining free the orientation of some macroscopic apparatus, will, but, as we show in the Appendix and in §10.1 must be the same as seen from arbitrary frames. of [1], adding randomness also does not explain (v) Finally, we note that the new proof involves the quantum mechanical effects described in our four inertial frames—A-first, B-first, F, and G. theorem. It is precisely the “semi-free” nature of This number cannot be reduced without weak- twinned particles, and more generally of entan- ening our theorem, since we want it to apply to glement, that shows that something very different arbitrary frames F and G, including for example from classical stochasticism is at play here. those in which the two experiments are nearly Although the FWT suggests to us that determin- simultaneous. ism is not a viable option, it nevertheless enables us to agree with Einstein that “God does not play Free Will Versus Determinism dice with the Universe.” In the present state of We conclude with brief comments on some of the knowledge, it is certainly beyond our capabilities to understand the connection between the free more philosophical consequences of the Free Will decisions of particles and humans, but the free Theorem (abbreviated to FWT). will of neither of these is accounted for by mere Some readers may object to our use of the randomness. term “free will” to describe the indeterminism of The tension between human free will and phys- particle responses. Our provocative ascription of ical determinism has a long history. Long ago, free will to elementary particles is deliberate, since Lucretius made his otherwise deterministic parti- our theorem asserts that if experimenters have a cles “swerve” unpredictably to allow for free will. certain freedom, then particles have exactly the It was largely the great success of deterministic same kind of freedom. Indeed, it is natural to classical physics that led to the adoption of deter- suppose that this latter freedom is the ultimate minism by so many philosophers and scientists, explanation of our own. particularly those in fields remote from current The humans who choose x, y, z, and w may of physics. (This remark also applies to “compati- course be replaced by a computer program con- balism”, a now unnecessary attempt to allow for taining a pseudo-random number generator. If we human free will in a deterministic world.) dismiss as ridiculous the idea that the particles Although, as we show in [1], determinism may might be privy to this program, our proof would formally be shown to be consistent, there is no remain valid. However, as we remark in [1], free longer any evidence that supports it, in view of the will would still be needed to choose the random fact that classical physics has been superseded by number generator, since a determined determinist quantum mechanics, a non-deterministic theory. could maintain that this choice was fixed from the The import of the free will theorem is that it is not dawn of time. only current quantum theory, but the world itself We have supposed that the experimenters’ that is non-deterministic, so that no future theory choices of directions from the Peres configuration can return us to a clockwork universe. are totally free and independent. However, the freedom we have deduced for particles is more Appendix. Can There Be a Mechanism for constrained, since it is restricted by the TWIN Wave Function Collapse? axiom. We introduced the term “semi-free” in [1] Granted our three axioms, the FWT shows that to indicate that it is really the pair of particles nature itself is non-deterministic. It follows that that jointly makes a free decision. there can be no correct relativistic deterministic

230 Notices of the AMS Volume 56, Number 2 theory of nature. In particular, no relativistic ver- choices of directions x, y, z, and w.1 There are sion of a hidden variable theory such as Bohm’s 40 × 33 = 1320 possible fields in question. For well-known theory [4] can exist. each such choice, we have a distribution X(FA,FB) Moreover, the FWT has the stronger impli- of flashes, i.e., we have different distributions cation that there can be no relativistic theory X1,X2,...,X1320. Let us be given “in advance” that provides a mechanism for reduction. There all such random sequences, with their different are nonlinear extensions of quantum mechanics, weightings as determined by the different fields. which we shall call collectively GRW theories (after Note that for this to be given, nature does not have Ghirardi, Rimini, and Weber, see [5]) that attempt to know in advance the actual free choices FA (i.e., to give such a mechanism. The original theories x, y, z) and FB (i.e., w) of the experimenters. Once were not relativistic, but some newer versions the choices are made, nature need only refer to make that claim. We shall focus here on Tumul- the relevant random sequence Xk in order to emit ka’s theory rGRWf (see [6]), but our argument the flashes in accord with rGRWf. If we refer to the proof of the FWT, we can see below applies, mutatis mutandis, to other rela- that we are here simply treating the distributions tivistic GRW theories. We disagree with Tumulka’s X(F ,F )[= X(x,y,z,w)] in exactly the same way claim in [7] that the FWT does not apply to rGRWf, A B we treated any other information-bit α that de- for reasons we now examine. pended on x, y, z, w. There we substituted all the (i) As it is presented in [6], rGRWf is not a de- values α1, . . . , α1320 for α in the response function terministic theory. It includes stochastic “flashes” θa(x, y, z, w; α). Thus, the functional hypothesis that determine the particles’ responses. However, does apply to rGRWf, as modified in this way by in [1] we claim that adding randomness, or a the recipe. stochastic element, to a deterministic theory does Tumulka [7] grants that if that is the case, then not help: rGRWf acquires some nasty properties: In some Λ Λ “To see why, let the stochastic element in a frame , “[the flash] fy will entail influences to putatively relativistic GRW theory be a sequence the past.” Actually, admitting that the function- of random numbers (not all of which need be al hypothesis applies to rGRWf has more dire used by both particles). Although these might consequences—it leads to a contradiction. For if, only be generated as needed, it will plainly make as we just showed, the functional hypothesis ap- no difference to let them be given in advance. plies to the flashes, and the first flashes determine But then the behavior of the particles in such a the particles’ responses, then it also applies to theory would in fact be a function of the informa- these responses, which by the FWT leads to a tion available to them (including this stochastic contradiction. element).” (ii) Another possible objection is that in our Tumulka writes in [7] that this “recipe” does statement of the MIN axiom, the assertion that a’s not apply to rGRWf: response is independent of B’s choice was insuf- “Since the random element in rGRWf is the set ficiently precise. Our view is that the statement of flashes, nature should, according to this recipe, must be true whatever precise definition is given make at the initial time the decision where-when to the term “independent”, because in no inertial flashes will occur, make this decision ‘available’ frame can the past appearance of a macroscopic to every space-time location, and have the flash- spot on a screen depend on a future free decision. es just carry out the pre-determined plan. The It is possible to give a more precise form of MIN problem is that the distribution of the flashes by replacing the phrase “particle b’s response is depends on the external fields, and thus on the independent of A’s choice” by “if a’s response is free decision of the experimenters. In particular, determined by B’s choice, then its value does not vary with that choice.” However, we actually need the correlation between the flashes in A and those precision only in the presence of the functional in B depends on both external fields. Thus, to hypothesis, when it takes the mathematical form let the randomness ‘be given in advance’ would that a’s putative response function θF cannot in make a big difference indeed, as it would require a fact vary with B’s choice. To accept relativity but nature to know in advance the decision of both deny MIN is therefore to suppose that an exper- experimenters, and would thus require the theory imenter can freely make a choice that will alter either to give up freedom or to allow influences to the past, by changing the location on a screen of the past.” a spot that has already been observed. Thus, he denies that our “functional hypothesis”,andsoalsotheFWT,applyto rGRWf.However, 1This unfortunately makes rGRWf non-predictive—it can we can easily deal with the dependence of the only find the flash distribution that “explains” either distribution of flashes on the external fields FA particle’s behavior when both experimenters’ fields are and FB , which arise from the two experimenters’ given.

February 2009 Notices of the AMS 231 Tumulka claims in [7] that since in the twinning [3] A. Bassi and G. C. Ghirardi, The Conway-Kochen experiment the question of which one of the first argument and relativistic GRW models, Found. Phys. flashes at A and B is earlier is frame-dependent, it 37(2) (2007), 169–185. follows that the determination of which flash influ- [4] D. Bohm, Quantum Theory in terms of “hidden” ences the other is also frame-dependent. However, variables, I, Phys. Rev. 85 (1952), 166–193. [5] G. C. Ghirardi, A. Rimini, and T. Weber, Unified dy- MIN does not deal with flashes or other occult namics for microscopic and macroscopic systems, events, but only with the particles’ responses as Phys. Rev. D34 (1986), 470–491. indicated by macroscopic spots on a screen, and [6] R. Tumulka, arXiv:0711.oo35v1 [math-ph] Octo- these are surely not frame-dependent. ber 31, 2007. In any case, we may avoid any such questions [7] , Comment on “The Free Will Theorem”, Found. about the term “independent” by modifying MIN Phys. 37 (2) (2007), 186–197. to prove a weaker version of the FWT, which nevertheless still yields a contradiction for relativistic GRW theories, as follows. ′ Authors’ Note: We thank Eileen Olszewski for MIN : In an A-first frame, B can freely choose any typesetting the paper and Frank Swenton for the one of the 33 directions w, and a’s prior response graphics. is independent of B’s choice. Similarly, in a B-first frame, A can independently freely choose any one of the 40 triples x, y, z, and b’s prior response is independent of A’s choice. To justify MIN′ note that a’s response, signaled by a spot on the screen, has already happened in an A-first frame, and cannot be altered by the later free choice of w by B; a similar remark applies to b’s response. In [7], Tumulka apparently accepts this justification for MIN′ in rGRWf: “... the first Ma thematicians rarely make it into the newspaper, much less into fashion flash fA does not depend on the field FB in a frame in which the points of B are later than those of A.” spreads. But on September 21, 2008, the This weakening of MIN allows us to prove a fashion section of the New York Times weaker form of the FWT: Sunday magazine carried a picture of An- FWT′: The axioms SPIN, TWIN, and MIN′ imply nalisa Crannell, a professor of mathemat- that there exists an inertial frame such that the re- ics at Franklin & Marshall College (and a sponse of a spin 1 particle to a triple experiment is book reviewer in this issue of the Notices). not a function of properties of that part of the uni- The magazine contacted Crannell saying verse that is earlier than the response with respect that it was doing a photo portfolio about to this frame. academics and had chosen her because This result follows without change from our she had received the Haimo Award from present proof of the FWT by taking F to be an the Mathematical Association of America. A-first frame and G a B-first frame, and applying “By phone, I learned that the ‘photo port- ′ F folio’ was really about fashion, which was MIN in place of MIN to eliminate θa ’s dependence G pretty funny because part of my Haimo on w and θb ’s dependence on x, y, z. ′ Award speech included the price tags of We can now apply FWT to show that rGRWf’s Λ the clothes I usually wear (US$1 or less),” first flash function (f of [4]), which determines y she said. a’s response, cannot exist, by choosing Λ to be the A crew of eight spent three hours frame named in FWT′. dressing Crannell and doing her hair and The Free Will Theorem thus shows that any makeup. One of them told Crannell he such theory, even if it involves a stochastic ele- loves mathematics and asked her some ment, must walk the fine line of predicting that for questions about fractals. The picture of certain interactions the wave function collapses to Crannell, which can be found on the Web, some eigenfunction of the Hamiltonian, without does not show the US$2,500 Gucci boots, being able to specify which eigenfunction this is. which Crannell called “pretty darned un- If such a theory exists, the authors have no idea comfortable”. “I was wearing my blue AMS what form it might take. ‘I love math’ bracelet that I’d picked up at MathFest, and the guy admired it so I gave References it to him,” Crannell recalled. “I didn’t get [1] J. Conway and S. Kochen, The Free Will Theorem, to keep any of the clothes they brought, Found. Phys. 36 (2006), 1441–1473. but he got to keep my bracelet!” [2] S. Kochen and E. Specker, The problem of hidden variables in quantum mechanics, J. Math. Mech. 17 (1967), 59–88.

232 Notices of the AMS Volume 56, Number 2 Book Review

Mathematics and the Aesthetic Reviewed by Annalisa Crannell

Mathematics and the Aesthetic like hubris or folly Nathalie Sinclair, David Pimm, and (or both) to trod this William Higginson, Editors ground once again. Springer (CMS Books in Mathematics), 2006 Who could touch US$59.95, 288 pages their eloquence? ISBN-13: 978-0387305264 What more could a body say? Mathematics and the Aesthetic is a heavy book. Enter Sinclair, I mean this in the literal sense: at 288 pages, it Pimm, and Hig- weighs 721 grams. The book has the same dimen- ginson. This trio sions as the little 206-page book on Fourier series of editors/authors that my mother studied from in 1959 [1], but into assembled a group that small space it packs almost half again the of scholars with number of pages and one-third again the mass. diverse academic This weight is a tangible sign of the care that the credentials: phi- authors, editors, and publisher used in putting the losophers, math book together. The high-quality paper is matched educators, and (yes) by a sense of attention to detail throughout. The research mathema- color pictures are carefully chosen and well pre- ticians. The authors’ sented; the text is easy to read. combined contributions are not (as I might have Which is all as it should be for a book with the originally supposed) additional propaganda to word “Aesthetic” in the title. convince the masses that math is beautiful. Rather, This is a daunting project to pull together, and each author explores the ways in which mathemat- there are many possible ways to botch the job. ics is an aesthetic experience. For some authors, When we try to describe the aesthetics of math- “aesthetic” translates into positive notions (like ematics—the discipline that gives us cohomology “elegance” or “beauty”); other authors use “aes- and nonlinear fourth-order partial differential thetic” in a more technical, neutral meaning of equations—it’s far too easy to become pretentious “relating to the senses and sensibility”. If the and wordy. I’ve often caught myself at the other second sense seems far from logic and from the extreme of sophistication, figuratively burbling in abstract reasoning of mathematics, we might use my beer: “No, man, it’s beautiful. No, really!” And instead the definition proposed by Judith Wechsler the middle ground, that space between pretension [3, page 2]: and exuberance, has been so famously traveled by the likes of Hardy and Poincaré, that it seems In its dealings with “things perceptible to the senses”, aesthetics comes to Annalisa Crannell is professor of mathematics at Frank- grips with relations: structure, context, lin & Marshall College. Her email address is annalisa. schemata, similarity/dissimilarity, con- [email protected]. sonance/dissonance. (About isolated,

February 2009 Notices of the AMS 233 simple, sense impressions aesthetics The aesthetic of “doing” arises in other chap- has little to say.) ters: Sinclair (Chapter 4) divides her analysis of “The aesthetic sensibilities of mathematicians” There are ten authors of nine chapters (eleven into three parts: how we evaluate mathematics, chapters, if you count the forward and afterward), how we generate new mathematics, and how we and often this mix would lend a hodge-podge feel are motivated to do various kinds of mathemat- to a volume. It’s true that this work didn’t escape ics. Schiralli (Chapter 5) creates parallels between completely from the bane of variable quality. Still, mathematics and art (and the aesthetics of each) more than in any other collection of essays I’ve by creating a page-long, bulleted list, each bullet read, the editors clearly worked hard with the au- beginning with an italicized verb (e.g., “create novel thors to ensure a sense of the whole; authors from or original symbolic patterns”). Jackiw (Chapter 7) one chapter often compare their own descriptions devotes his entire chapter to “dynamic geometry” to those that appear in other chapters, and navigat- and to ways in which mathematicians understand a ing through the book is easy to do. figure by moving its parts. Henderson and Taimina Are there general themes that emerge? (Chapter 3) address the noun/verb issue explicitly One of the things that struck me as I read in their essay on “Experiencing meanings in geom- through these chapters—particularly through the etry” (page 83): first half of the book—was the recurring theme of describing the doing of mathematics, rather …In fact, rarely do we find proofs, in than describing the mathematics itself. We often and of themselves, to be aesthetic ob- articulate the usefulness of doing mathematics (for jects. Instead, we locate the aesthetic example, telling our students that “mathematics value of mathematics in the coming- is not a spectator sport”). But these authors move to-understanding, in the integration of beyond utility to aesthetics, in ways I’ll elaborate experience and meaning. below. Their collective perspectives made me wish But this emphasis on verbs is a motif that I for a few new good verbs. There is no good verb for myself have imposed on the reading of this book. “to do beautiful things”, for example: beautify, as a It would be fairer to the book for me to sketch its transitive verb, doesn’t quite work, since it requires outline and give a quick tour of the content of its that something else get beautified, rather than im- chapters. Here is an overview, which I’ll follow with plying the action itself is beautiful. And similarly, a deeper examination of one or two of the more there’s no good verb for “to do mathematics”. provocative chapters. This impoverishment of vocabulary strikes me The editors divide the main body of the work as a shame. The authors in this volume frequently into three-chapter groupings, which fit into three used theorems and proofs (well-known, surprising, sections: first, mathematics as an aesthetic subject; or personally dear) to illustrate their points, but second, an explanation of “the aesthetic dimen- they just as often described the experiences of sion of mathematics”; and third, a description grappling with mathematics, of puzzling through of how both of these subjects fit into the study it, and of making sudden sense of previously con- of aesthetics in other disciplines. If the first two fusing concepts. Poincaré famously described his sections seem similar, I will add that locating the own epiphanic experience of completing a perplex- emphasis on mathematics (in the first case) or ing proof, and many mathematicians are familiar on aesthetics (in the second) is key: Section A is with that kind of “aha” gift of insight. To me an authored by research mathematicians who look even more touching description of the doing of at mathematics through their own perspectives; mathematics is Doris Schattschneider’s descrip- Section B is authored by mathematics educators tion (page 56) of pleasure in hammering together and philosophers who look at mathematics, so to some not-so-beautiful mathematics. After describ- speak, through other people’s eyes. Each of the ing in some particular detail why the proof she had three sections comes with a one-page introduction worked on was neither elegant, nor ingenious, nor from the editors. generalizable, nor insightful, nor illuminating, she In addition, the editors include Chapters Alpha continued on: and Omega to introduce and close out the book. Yet, I received a measure of satisfaction Chapter Alpha was for me a welcome introduction to the history that precedes this book, telling the in proving this result. I had believed it story of mathematical paradigms from the time was true and now it was proven to be of the Pythagoreans through St. Augustine, Gauss, true. And, along the way, I saw some Hadamard, Russell, and others, and then pointing connections that I could not have seen toward the future. (I’ll pick a fight with Chapter without actually going through the Omega in due time.) process … Section A (“The mathematician’s art”) is prob- And then she delightedly shares some of the ably the most familiar and comfortable material connections she discovered. to readers of the Notices. Jonathan Borwein leads

234 Notices of the AMS Volume 56, Number 2 off with a chapter that takes a, “Hey! Look at this ordered arrangements of numbers) connected cool proof!” approach. He doesn’t use those words the subject with “the very fabric of the know- or even exclamation points, which would be too able world and their efforts to find the principles campy, but his enthusiasm shines through. He unifying that fabric in the mathematical-aesthetic shares some of his favorite insights into the num- ratio of harmonic intervals” (page 119). He contin- ber pi, and he demonstrates some elegant geomet- ues in this vein to describe how later philosophers ric proofs of the almost-without-words variety. such as Wittgenstein and Kant used “numbers as Then Doris Schattschneider takes over with a cognitive scaffolding” for understanding natural chapter that—in true mathematical style—leads phenomena. William Higginson finishes the sec- off with illustrative examples that provide the con- tion with a chapter that flits among stereotypes of text and motivation for a more general aesthetic mathematicians, popularizations of mathematics, framework. She starts with some of the histori- and the anthropological and historical basis for cal, classical theorems that have shaped our own mathematical capacity. mathematical culture and then lists five attributes Section C (oddly titled “Mathematical agency”) of mathematical work that we claim are beautiful contains three essays that take interdisciplinary (page 43): elegance, ingenuity, insight, connections, approaches to examining aesthetics. This section and paradigm. (My art colleagues, I think, would is a wild ride. It begins with an essay on the didac- appreciate this list.) Throughout, she uses specific tics of dynamic geometry by Nicholas Jackiw (the pieces of mathematics (like an elegant proof of the chief technology officer of KCP Technologies and arithmetic-geometric mean inequality) to illustrate original designer of the Geometer’s Sketchpad). It these ideas in context. concludes with an essay by the late Dick Tahta that David Henderson and Daina Taimina close out takes a Freudian approach to “the perennial debate this section by examining our “need” for mean- about the nature of mathematical objects” (page ing. They illustrate this need through mathemati- 204) and all that this implies about our anxiety cal examples and paradoxes, comparing various regarding our mothers. Sandwiched between those definitions of the concept “line” (e.g., “shortest two pieces sits something pure and holy. distance” versus “no wiggles” versus “circle of David Pimm’s essay (“Drawing on the image in infinite radius”). Correctness of the results alone, mathematics and art”) caught me by surprise and they maintain, feeds the belly but not the soul: kept me up late reading it. In it, he describes how one particular aesthetic (the purity of iconoclasm) For example, [a 1973 paper by Hender- permeated and became ritual in both the Bourbaki son] has a very concise, simple (half- movement and in the reformed English Church. page) proof. This proof has provoked He contends that notions of “purity” (in the re- more questions from other mathema- ligious and also in the “pure math” sense) led to ticians than any of his other research the same sense of iconoclasm: rejection of figures papers, and most of the questions were (geometric or human) and an attempt to get at of the sort: “Why is it true?”, “Where did Truth directly, without any mediating interference. it come from?”, “How did you see it?” There is more; it is worth reading. I am unabash- They accepted the proof logically, yet edly unfamiliar with the subject and don’t pretend were not satisfied. (page 66) to have the slightest idea of the correctness of his If Section A starts with the math and then de- argument. And yet I very much appreciated this scribes where aesthetics fits in, then Section B (“A one essay which homed in so narrowly on a single sense for mathematics”) does the reverse. Nathalie historical mathematical movement and which Sinclair uses interviews with a half-dozen living chose one single particular aesthetic ideal, and tied mathematicians, co-mingled with the writings of the two together so neatly. And fittingly, if surprise many other prolific mathematicians, to explore and insight are aesthetic qualities, then I have all aesthetic considerations in mathematics. She is the philosophical justification I’d need to say this methodical and clear, and I enjoyed her insights, essay is an aesthetic work. even as I felt a bit like a biological specimen dis- Why, then, did Pimm and Sinclair have to muck played under a microscope. For example, when around in Chapter Omega? Darn it, the review she describes standard ways that mathematicians would have been lovely if I could have stopped approach solving problems, she includes “playing” one paragraph ago—just as this book would have and “establishing intimacy”, perhaps by naming or been lovely if it stopped one chapter earlier (or claiming the objects involved: my triangle. Maybe two, depending on how you feel about Freud and next time I’ll lower the blinds. maternal separation anxieties). Chapter Omega Martin Schiralli builds on Keith Devlin’s book on comes in several unhappy pieces, three of which mathematics and pattern [2] by adding a consider- I lay out here (in a butchered and, I admit, unfair ation of the aesthetic connections between these way). The first is that mathematics is dehuman- two concepts. He notes that the Pythagoreans’ con- izing (to be more specific, “decontextualized”, ception of arithmetic (as understood to represent “depersonalized”, and “detemporalized”), a fact

February 2009 Notices of the AMS 235 the authors conclude from the way we write our talks at a conference, this is an odd and paradoxi- research articles. Second, the mathematical mind cal omission. is a melancholy one, for which the most striking But perhaps I am being too harsh—perhaps I am evidence is the famous etching Melencolia I by complaining that I didn’t get an action toy in my Albrecht Dürer. Dürer was melancholy. True, he box of Cracker Jack, and forgetting to be grateful was an artist, but (as the authors take pains to for the secret decoder ring that did come with my point out) he was an artist who liked mathematics. snack. Mathematics and the Aesthetic is a thought- Third, there is some connection between math- ful collection of essays, bound together with care- ematics and autism, particularly in the way we ful organization, attention to small details, and (don’t) relate to other people. The authors wend even a bit of elegance. their way through the argument for this connection Which is all as it should be for a book with the by noting that we seem to have similar modes of word “Mathematics” in the title. reasoning, but also (on pages 240–241): References • some famous mathematicians might have had [1] Ruel Churchill, Fourier Series and Boundary Value autism (that is, some psychologists have written Problems, McGraw-Hill, New York, NY, 1941. speculative articles with post hoc diagnoses of [2] Keith Devlin, Mathematics: The Science of Patterns: a half-dozen mathematicians); The Search for Order in Life, Mind and the Universe, Henry Holt & Co., New York, NY, 1994. •by implication, most mathematicians are defi- [3] Judith Wechsler, editor, On Aesthetics in Science, cient at relating to other people, and MIT Press, Cambridge, MA (1978). •this might “be part of the explanation” about why women are less likely to be mathematicians. Well, faugh. Leaving aside completely questions of scholar- ship and evidence, this chapter stands at odds with the rest of this book. It certainly is no summary of the previous essays, and indeed, it contrasts most markedly with the writings of Section A (written by the research mathematicians themselves). For me, this chapter was particularly surreal because I read it while I was at the 2008 MathFest. There, Christine Stevens spoke about the more- than-1000 Project NExT Fellows and about the impact they have had on the mathematical community—and about how they have had this impact precisely by building and strengthening communities. Erik Demaine gave a series of standing-room- only talks about the mathematics of folding, and he wove in touching stories of working with his father and with his many coauthors. “The main point of these talks,” he repeated often, “is that Mathematician Jason Brown of Dalhousie you ought to have fun.” Sixteen hundred people University in Halifax, Canada, was in the joined together in a celebration of mathematics, news for his work analyzing the opening in meeting new people, and in reacquainting with chord of the Beatles’ song “A Hard Day's old friends. Night”. It was known that most of the And if this book has any glaring holes, it is chord was played by George Harrison, but perhaps this. Aside from a brief nod from Sinclair the exact nature of the chord remained (two paragraphs) that social factors can have a a mystery for forty years. Brown used a motivating influence on the kinds of mathematics Fourier transform to analyze the frequen- we choose to do, there’s little mention of the col- cies and solve the mystery. He found an laborative aspects of mathematics. Nobody writes F note in the opening sound that could about the aesthetics of co-authoring, the joy of not be played on Harrison’s 12-string mentoring junior faculty, the sheer hero-worship guitar and deduced that the note was that impels us to follow others, nor the invigora- part of a piano chord played along with tion that can come from bouncing our ideas off the guitar. The Halifax Chronicle Herald of other people. Nobody writes about talking out has more about Brown and his research loud about mathematics, nor of hearing others at http://thechronicleherald.ca/ talk about it. For a book that arose—as the first Front/1087119.html. sentence of the preface tells us—from a series of

236 Notices of the AMS Volume 56, Number 2 Book Review

Group Theory in the Bedroom, and Other Mathematical Diversions Reviewed by David Austin

Group Theory in the Bedroom, and Other section in which Mathematical Diversions Hayes reflects on Brian Hayes the original work, Hill and Wang, 2008 scrupulously owns US$25.00, 288 pages up to errors, and ISBN-13: 978-0809052196 discusses responses received from read- While driving across my home state of Michigan ers. not so long ago, I noticed that the format for the Let’s begin by state’s license plates had changed. The old format looking at the essay, had three letters followed by three digits; some- “Dividing the conti- time recently, a fourth digit was added. Wondering nent”, appropriately why the change had been made, I figured that the placed in the middle old format had 263 1000 possible designations of the collection. · and quickly estimated that this gave around 16 Hayes describes a million possibilities. I knew that the population recent driving trip, of Michigan is about 10 million so I could see, and the question assuming license plates are not reused, how we that arose in his mind as he drove over the conti- could be running low on plates either now or in nental divide on the Idaho-Montana border: What the near future. Maybe this was a good time to add is the mathematical nature of the continental another digit. divide and how would one determine its location? Mathematicians do this kind of thinking fre- Written in the first person, the essay consists of quently. There’s no deep mathematics involved, his evolving thoughts as his journey continues but our comfort with computation can help explain (“Somewhere in North Dakota or Minnesota …I observations we make as well as make a long drive finally began to settle on an idea….”). a little less tedious. Eventually, Hayes begins searching for an In his wonderful new book, Group Theory in the algorithm to detect the continental divide. Inter- Bedroom, and Other Mathematical Diversions, Brian estingly, his resources are limited; being on the Hayes shows how pleasurable this kind of thinking road, he is away from a computer and a library. can be and the surprising places to which it can Thinking is his only tool. Continuing on, Hayes lead. The book collects and slightly reworks twelve shows us several possible algorithms, which of Hayes’ essays, which originally appeared over the initially seem promising but are seen after further thought to be deficient, before arriving at an espe- last decade in the The Sciences and American Sci- cially appealing, elegant solution. entist. Each essay also includes an “Afterthoughts” Back at home, Hayes continues the project by acquiring a digital elevation map and implement- David Austin is professor of mathematics at Grand Valley ing his algorithm. Sure enough, the continental State University. His email address is david@merganser. math.gvsu.edu. divide shows up just where we expect. He also

February 2009 Notices of the AMS 237 searches the literature on this subject, finding early Topics of other essays include: papers by Arthur Cayley and James Clerk Maxwell •a remarkable working clock, constructed with and comparing their thoughts to his own. Hayes gears in the 1800s, built to be accurate for at least also finds that, in addition to the expected work in 10,000 years. Hayes deftly relates this to the crisis geography, this problem is also important in image that was predicted to follow the Y2K phenomenon, analysis and artificial vision. a crisis thought to result from software engineers Relating these thoughts as part of a long trip who failed to imagine their code would be running serves Hayes’ larger purpose. As he writes in the in a few decades; “Afterthoughts” section: “In telling the story, I •an investigation of randomness, whether it wanted to focus not so much on the solution to really exists, and what it means that mathematics the watershed problem as on the process by which has not found a way to create randomness; people go about finding or inventing solutions. •a survey of early attempts to explain the ge- Where do the ideas come from? How do we evalu- netic code, the means by which a string of nucleo- ate alternatives? How do we know when to stop?” tides on a DNA molecule represents a sequence of This story is about traveling rather than arriving, amino acids. Nature’s code is much less elegant and we feel involved in it. At several points, I put than the mathematical ones first proposed, but in the book down and developed an outline for my the end nature seems to have gotten it right; own algorithm. •an economic model of the distribution of While the other essays do not originate in a wealth based on the kinetic theory of gases. Para- long car trip, many of them read like travel doxically, an economy based on theft leads to a essays, as Hayes takes us on expeditions through more equitable distribution of wealth than one landscapes surrounding interesting mathematical based on fair trading; questions. Sometimes, such as when the conti- •the partitioning problem, and what it means nental divide appears before our eyes, we realize for a problem to be hard; the joy has been in the journey as much as the •name spaces, such as radio station call letters destination. Other times, these investigations and airport codes (and, yes, license plates), and lead to surprising questions that reflect more how they fill up; broadly on who we are, what we value, and the •ways in which the base three number system nature of mathematics. is superior to the more familiar binary and decimal Another essay, “Statistics of deadly quarrels”, systems; presents a study of the number of human-caused •how it can be tricky to determine if two things casualties in recent history. Hayes begins by in- are really the same; troducing us to Lewis Fry Richardson, a British •and night thoughts on how to flip a mattress meterologist who, after serving in the first world periodically so that all possible orientations are war, began to apply the mathematical techniques used equally. This essay lends its title to the book he had used in meterology to a study of war. as well. Richardson painstakingly attempted to tally all As may be seen, the essays, for the most part, deaths between 1820 and 1950 attributable to the originate in “real world” issues. Hayes writes the actions of another person. This would, of course, “Computing Science” column in American Scientist, include all war deaths as well as all murders and so it’s no surprise that many of the topics have a suicides. (It is easy to speculate that Richardson, computational component. Indeed, Hayes is quick perhaps haunted by the horrors he witnessed in to write some code to test an idea, and some the war, was hoping to explain what he had readers, like this one, will no doubt be inspired to seen.) follow suit. It is not expected, however, that the au- Of course, this is a daunting task that is neces- dience shares this interest in computing. Instead, sarily incomplete. However, a statistical analysis computation is used as a means to address other of the data is fascinating for what it does not issues. In his blog, http://bit-player.org/, show. Factors that might be thought to influence Hayes accurately describes some of his work as the outbreak of war—such as countries sharing a “inquisitive programming”, which he defines as common language or engaging in an arms “computer programming [used] as a tool for ex- race—are seen to be statistically insignificant. ploring, experimenting, and problem-solving”. Instead, the most striking observation is that the Most of the essays contain interesting bits of number of new wars per year closely follows a what could be called trivia, though they never Poisson distribution, which would follow if the seem superfluous. There are often interesting bio- probability of a war breaking out at any given graphical sketches of little-known players as well time is constant. This does not, of course, imply as tidbits such as how random numbers are used that individual wars occur randomly; rather, it ap- in the Ethernet networking protocol; the origin of pears that war is a perpetual feature of our human the equals sign; and why Brocot, a French watch- existence. maker, was led to discover what we now call the

238 Notices of the AMS Volume 56, Number 2 Stern-Brocot tree. The writing is uniformly good, exceptionally clear, and with abundant humor and About the Cover humanity. Hayes writes with a refreshing openness; Long divide as part of his colloquial style, he is quick to admit errors and naive ideas. This month’s cover was produced by Brian Group Theory in the Bedroom should be acces- Hayes, and is derived from images he in- sible to a wide audience. Hayes uses almost no cluded in the column “Dividing the Conti- mathematical notation and assumes relatively little nent” that he wrote for the November 2000 mathematical knowledge. For instance, when e is issue of American Scientist (available at used at some point, Hayes writes, “e is the number http://www.americanscientist.org/ 2.718 (known as Euler’s number).” A formula for issues/pub/dividing-the-continent/). the Poisson distribution is given, but Hayes quickly It illustrates how the algorithm he used gives a lucid interpretation of its meaning. proceeds to find the continental divide of This is not a book that aims to teach grand North America, drawn as the thin red trail of mathematical theory or to follow in the footsteps pixels in the final image. Basically, it floods of giants. So what is its aim? Asking the question the ocean basins and keeps track of where almost feels wrong. Hayes seems to be enjoying they meet as the flood rises. himself so much, and the reader is so involved, that Brian Hayes has been writing the column no greater goal seems required. These are, after all, “Computing Science” for American Scientist “mathematical diversions”. What I found, however, for many years, and it is a constant source is that the essays, taken as a whole, demonstrate of interesting mathematical and computa- convincingly the joy of mathematical thinking and tional ideas. Some of his columns have been the real power available when it is applied to more collected in the book Group Theory in the general inquiries. Bedroom, reviewed by David Austin in this As much as any book I can name, Group Theory issue of the Notices. The elevation data for in the Bedroom conveys to a general audience the Hayes’s maps come from http://www.ngdc. playfulness involved in doing mathematics: how noaa.gov/mgg/global/etopo5.HTML. questions arise as a form of play, how our first He writes: “The basic idea is to raise the attempts at answering questions usually seem level of both oceans in stages until the waters naive in hindsight but are crucial for finding even- meet. The line along which they meet is the tual solutions, and how a good solution just feels continental divide. This physical process is right. As Hayes writes, “I’m not a mathematician, easy to describe, but that’s because water but I’ve been hanging out with some of them long performs an extraordinary parallel compu- enough to know how the game is played.” In ad- tation when it seeks its own level. Trying to dition, Hayes’ writing, with its openness, invites emulate that process in a sequential, digital the reader to participate actively. I often felt I was computer takes considerably more trouble.” having a conversation, and at times an argument, He also tells us that an animated version with the author. of the process can be found at http:// We often hear it said that more students need to bit-player.org/bph-publications/ take more mathematics courses, even if they never AmSci-2000-11-Hayes-Cont-Divide/ subsequently use the content, for mathematics animate.html. helps build general problem-solving and critical thinking skills. This argument seems dicey to me: —Bill Casselman, Graphics Editor why should mathematics, as least as traditionally ([email protected]) taught, foster critical thinking any more than philosophy or literature or physics? Without addressing the issue explicitly, Group Theory in the Bedroom presents a more compelling argument for the importance of mathematics. Whether it develops general skills or not, mathematics is a fundamental tool in an intellectual toolkit and is crucial for making sense of the world around us.

February 2009 Notices of the AMS 239 WHATIS... ? a Skein Module? W. B. Raymond Lickorish

Consider all formal linear sums of oriented links encircling T , in as simple a way as possible, r in a 3-manifold M. Coefficients are to be in times. Finding an easy description of the skein Z[v−1, v, z−1, z], the Laurent polynomials in v module of an arbitrary 3-manifold is usually not and z. Impose on this all relations of the form possible. However, any orientable 3-manifold M −1 3 v L+ − vL− = zL0, where L+, L−, and L0 are three can be formed from S by surgery, by removing links identical except near a point where they are and replacing differently solid tori fattening a link as in Figure 1. The result is the oriented linear L in S3. Evaluation of a certain carefully chosen skein module of M. element of the skein module of T placed around every component of L, can produce “quantum” L L L invariants of M. The intricate details of this are in + - 0 [3]. An evaluation of elements of skein modules, linear sums of links (or later, tangles) in some Figure 1. The only differences in L+ , L− , and L0 . configuration, will always mean the multilinear sum of all evaluations of unions of summands. Evaluating a link in terms of a base of a skein A link is, of course, a finite collection of disjoint module can be seen as a partial calculation of a simple closed curves (strings) in M, two links being link invariant. In a relative version of the above, the same if one can be moved to become the other M has non-empty boundary ∂M containing 2N without breaking the strings (such a movement is specified “fixed” points; N of these have an inwards technically an ambient isotopy). A fundamental orientation and N an outwards one. The theory 3 theorem is that, when M is ordinary 3-space R , proceeds as before using tangles instead of links. A 3 or the 3-sphere S , this skein module is free of tangle is a disjoint union of oriented simple closed dimension one with base the unknot U. Thus the curves with N oriented arcs joining in pairs the coordinate, or evaluation, of an oriented link L 2N specified points. Two tangles are the same if with respect to U is a polynomial invariant P (v, z) L one can be moved to the other keeping ∂M fixed of L. during the movement. In a famous example of J. H. Let T be the solid torus A × [0, 1], where A Conway, M is a ball with four specified points. The is an annulus. The union of a link in the solid skein module of M is then 2-dimensional with base torus A × [0, 1 ] with a link in A × [ 1 , 1] is a link in 2 2 the two tangles t and t of Figure 2. Any 2-string T . This defines a product, and the skein module 0 ∞ tangle in the ball can be expressed as a linear of T becomes a commutative algebra. A short combination of t and t . The tangle t shown argument, using the above relation to “change 0 ∞ 2n with 2n crossings is v2nt +zv(v2n −1)(v2 −1)−1t , crossings”, shows this is generated as an algebra 0 ∞ for example, and wherever a copy of t occurs in by {L : r ∈ Z}, where L is a single string steadily 2n r r a calculation this can be substituted. If a sphere 3 W. B. Raymond Lickorish is Emeritus Professor of Geomet- S cuts a knot K contained in S in four points, ric Topology at the University of Cambridge. His email it divides K into a tangle in the ball inside S address is [email protected]. and another in the ball outside. The polynomial

240 Notices of the AMS Volume 56, Number 2 unknot U. The U-coordinate of a link L is, up to a

Figure 2. t0 and t∞ are a module base.

PK (v, z) can be found by expressing these tangles in terms of the bases of the two balls and combining the bases together with a simple 2 × 2 Figure 4. Kauffman bracket relations. matrix. Now note that a π-rotation about one of the three coordinate axes of Figure 2, together with factor, the Jones polynomial P (A−4,A−2 − A2) of reversal of arrows if needed, leaves the two base L L. This formulation of L. H. Kauffman [1] led to the elements unchanged. Thus, if K is changed to K0 main applications of the Jones polynomial. by removing the tangle inside S, giving it one of The Kauffman Bracket skein module of the the three π-rotations and replacing it, PK (v, z) and 0 solid torus T is just the polynomial algebra over P 0 (v, z) are identical. The change from K to K is K Z[A−1, A], a generator being one untwisted curve, Conway’s mutation. He invented skein theory in α say, encircling T once. Depict the ball B with the 1970s when the Alexander polynomial (t) ∆L 2n boundary points as a rectangle with n points was the only relevant oriented link invariant (where on each of the left and right sides. Concatenation − 1 1 ∆L(t) = PL(1, t 2 − t 2 )). Conway noted that the of rectangles makes the skein module of B into only two (distinct) 11-crossing knots with ∆K (t) = 1 an algebra. It is the nth Temperley-Lieb algebra of ! are related by mutation. 2n For a ring R and any 3-manifold M, a skein dimension 1 but generated as an algebra n+1 n module is, then, just a quotient of the free R- by n elements {1, e , e , . . . , e } shown in Figure module generated by all tangles in M. In practice 1 2 n−1 5. This algebra has a unique element f (n), the Jones- the type of quotient must be chosen with care. A second linear skein module can be constructed from formal linear sums of unoriented links using the ring Z[z−1, z] and all relations of the form shown in Figure 3. The same fundamental theorem then holds. Requiring links and tangles to be Figure 5. Temperley-Lieb generators.

(n) (n) Wenzl idempotent, such that f ei = 0 = ei f and (f (n) − 1) belongs to the algebra generated by { } (n) (n) = (n) (n) Figure 3. Skein relation without orientations. e1, e2, ..., en−1 , (so f f f ). Placing f in a solid torus T , and connecting the n points on the left to those on the right directly around T , “framed”, by the giving at each point of a normal produces Sn(α), a Chebyshev polynomial in α. If direction (which in diagrams will always point at Sn(α) contained in T is placed, without twisting, the observer), enables the ring to be extended to around the unknot and interpreted in the skein become Z[a−1, a, z−1, z]. module of S3, its coordinate (with ∅ as base) is n 2(n+1) −2(n+1) 2 −2 −1 The next example is altogether more amenable. ∆n = (−1) (A − A )(A − A ) . Thus th It has indeed been calculated for lens spaces ∆n = 0 if A is chosen to be a complex (4n + 4) and certain knot complements and generalised by root of unity. Then the (normalised) evaluation Pn−1 “categorification”. It is the Kauffman Bracket skein of r=0 ∆r Sr (α) placed around each component module of a 3-manifold M, all formal Z[A−1, A] of a surgery link defining a 3-manifold, gives a linear sums of framed unoriented tangles in M 3-manifold invariant. modulo all relations of the forms of Figure 4 (i) The evaluation of a link with Sc(r)(α) placed and (ii) (type (iii) is a consequence). Here (i) refers around its r th component is the Jones polynomial to the union of a tangle L with an unknot in a ball of the link coloured by the function c. The form disjoint from L, and in (ii) the tangles are identical of the above 3-manifold invariant gives motivation 3 except where shown. In R one can project to a to the calculation of coloured invariants. As Sn(α) plane and use (ii) to lose crossings, then (i) to lose is just f (n) with its end points joined around a closed curves. The upshot is that the module for solid torus, this leads to consideration of config- R3 is one-dimensional with base the untwisted urations of many f (n)s joined together in subtle

February 2009 Notices of the AMS 241 In the Kauffman Bracket skein module of the ball with four specified boundary sets of a, b, c, and d points, consider the submodule of all skeins having f (a), f (b), f (c), and f (d) adjacent to these sets (see Figure 7). It is not hard to show that all the elements [(a, b)j(c, d)], with both triples compatible, form a base of this submodule. So do the elements [(b, c)i(d, a)]. The terms in the change of base matrix, defined na b i o by [(a, b)j(c, d)] = P [(b, c)i(d, a)], i c d j are called “6j-symbols”. A cumbersome closed

Mathematical Gates. The main entrance to the Centre for Mathematical Sciences in Cambridge is sealed by iron gates. Medallions in these gates show the only two knots with at most eleven crossings, other than the unknot, that have trivial Alexander polynomial. One Figure 7. The ball with four point sets. gate shows the knot studied by S. Kinoshita and H. Terasaka, whilst the other gate shows formula is known for them. An arc labelled a the knot discovered by J. H. Conway in his over-crossing one labelled b has jth coordinate classification of eleven-crossing knots. Related a+b−j −1 a+b−j+(a2+b2−j2)/2 as they are by one of Conway’s mutations they (−1) 2 ∆j θ(a, b, j) A with re- cannot be distinguished by any invariant spect to base {[(a, b)j(a, b)]}. Using this, an based on skein theory. The medallions were expression for any coloured Jones polynomial can created by John Robinson and donated by be derived in terms of the ∆n, the θ(a, b, c), and Damon de Laszlo and Robert Hefner III. the 6j symbols. Finally, the evaluation τ of the edges of a tetrahedron labelled with {c, b, j} around a face and {a, d, i} on the edges opposite is ways. Such configurations are drawn as labelled na b i o −1θ(i, b, c)θ(i, a, d) . When A4n+4 = 1, planar trivalent graphs, possibly with crossings, ∆i c d j where an integer a ≥ 0 labelling an edge indicates the Turaev-Viro 3-manifold invariant is the presence of a copy of f (a) in a strings parallel XnY Y Y o kv θ(sf ) τ(st) , to the edge. A vertex, where edges labelled a, b, ∆se b s e f t and c meet, denotes the element of the skein − module of a ball with a + b + c specified points where k = (A2 − A 2)2/(−2n − 2). Here e, f , and shown in Figure 6 (i) where x + y = c, y + z = a, t are the edges, faces, and tetrahedra of a tri- and z + x = b. For this to exist, {a, b, c} must be angulation with v vertices, and s runs through edge-labellings compatible around any face, with face sums at most 2n − 2. A tetrahedron with labelling dual to s on t (three labels at a vertex now encircle a face) is denoted stb .

Further Reading [1] L. H. Kauffman, Knots and Physics, World Scientiﬁc, 1991. Figure 6. Triad and graph for θ(a, b, c). [2] W. B. R. Lickorish, Quantum invariants of 3- manifolds, Handbook of geometric topology, (R. J. Daverman and R. B. Sher, eds.), Elsevier, 2002, pp. compatible, meaning that a+b+c is even, a ≤ b+c, 707–734. [3] Y. Yokota, Skeins and quantum SU(N) invariants of ≤ + ≤ + b c a, and c a b. The labelled graph of 3-maniolds, Math. Ann. 307 (1997), 109–138. Figure 6 (ii) evaluates to

+ + ! − ! − ! − ! θ(a, b, c) = ∆x y z ∆x 1 ∆y 1 ∆z 1 , ∆y+z−1!∆z+x−1!∆x+y−1! where ∆n! denotes ∆n∆n−1∆n−2...∆1.

242 Notices of the AMS Volume 56, Number 2 MathematicsMATHEMATICS Faculty Position In a pioneering international initiative, the Weill Cornell Medical College (WCMC) established the Weill Cornell Medical College in Qatar (WCMC-Q) with the sponsorship of the Qatar Foundation for Education, Science and Community Development. WCMC-Q is located in Doha, Qatar, and in its seventh year of operation, its inaugural class having graduated with Cornell MD degrees in May 2008. WCMC-Q seeks candidates for a full-time senior level faculty position to teach in Doha in the Pre-medical Program, with major responsibility for teaching mathematics to premedical students. The two-year Pre-medical Program is designed to prepare students for admission to the WCMC-Q Medical Program. Intensive and challenging, this two-year program has been specifically prepared for students in the Middle East. It provides them with instruction in subjects that comprise the pre-medical requirements of most medical colleges in the US. The successful candidate will teach one course per semester at the level of college calculus and introductory statistics. In addition, he/she will participate in student academic advising, committee work, and the academic life of WCMC-Q. Research funding support is available and active participation in relevant research will be encouraged. Qualifications include a Ph.D. in Mathematics, demonstrable teaching skills, and teaching experience at the college/university level. Candidates are expected to have experience in the American higher education system and must be willing to relocate to Doha, Qatar for the duration of the appointment. Academic rank and salary are commensurate with training and experience and are accompanied by an attractive foreign-service benefits package. Qualified applicants should submit a curriculum vitae and a letter of interest outlining their teaching and research experience to: http://job.qatar-med.cornell.edu * *Please select the appropriate position under the Academic options and indicate job # 08-wcmcq-MT BAYARD Cornell University is an equal opportunity, affirmative action educator and ADVERTISING AGENCY, INC employer. Details regarding the WCMC-Q program and JOB #: B facilities can be accessed at: www.qatar-med.cornell.edu CLIENT: Weill Cornell The screening of applications will begin immediately and continue until PUBS: Notices suitable candidates are identified. Please note that due to the high volume SIZE: 4.625” x 9.5” of applications, only short-listed candidates will be contacted. Service is DATE: 11-11-08 expected to begin in August 2009. COST: fm ARTIST: Bz Short-listed candidates will be asked to provide names of three references. COMP: Oz REV. 0 OK to Release Tribute to André Lichnerowicz (1915–1998) Yvette Kosmann-Schwarzbach

Thirty years ago: Annals of Physics, 111. Deforma- that were published by Yvonne Choquet-Bruhat, tion quantization was born. This sequence of two Marcel Berger, and Charles-Michel Marle in the articles [BBFLS 1978] had been preceded by several proceedings of a conference held in his honor on papers written by Daniel Sternheimer, who has just the occasion of his seventieth birthday [PQG 1988], addressed you,1 by Moshé Flato whose memory or his portrait and an interview that appeared in Daniel has just recalled and whose personality and a handsome, illustrated volume describing the work in mathematics and physics were so remark- careers of twenty-eight of the most important able, and by André Lichnerowicz. French scientists of the twentieth century, Hom- Who was Lichnerowicz? To his students, he mes de Science [HdeS 1990]. Finally, and sadly, was “Lichné”. To his friends, he was “André”. As a scientific obituaries appeared in the Gazette des mathematician, mathematical physicist, reformer Mathématiciens [Gazette 1999], and they were of the French educational system and its math- quickly translated for the Notices of the AMS [No- ematical curriculum, and as a philosopher, he was tices 1999] because Lichnerowicz was as famous known to the public as “Lichnerowicz”, a man of outside France as he was within it. Other obituaries vast culture, an affable person, a great scientist. appeared in the Journal of Geometry and Physics, There are many ways to approach André Lich- of which he had been one of the founders, and in nerowicz. One would be to read all his more than many other journals. three hundred sixty articles and books that have Lichnerowicz had an exceptional career. He was been reviewed in Mathematical Reviews (MathSci- a student from 1933 to 1936 at the École Normale Net), another would be to read only his personal Supérieure in Paris where he studied under Élie choices among them, those that were published Cartan, who had a lasting influence on his math- by the Éditions Hermann in 1982 as a 633-page ematics. He completed his thesis, written under book, Choix d’œuvres mathématiques [L 1982]. You the direction of Georges Darmois, in 1939, and was can read the summaries of his work up to 1986 named professor of mechanics at the University of Strasbourg in 1941. Because of the war, the faculty Yvette Kosmann-Schwarzbach is professor of mathemat- of the University of Strasbourg had already moved ics, retired from Université de Lille and Centre de Mathé- to Clermont-Ferrand in order to avoid functioning matiques Laurent Schwartz, École Polytechnique, France. under the German occupation. However in 1943, Her email address is [email protected]. 1 the Germans occupied Clermont-Ferrand as well, This tribute was delivered at the conference “Poisson and there was a wave of arrests in which Lichnero- 2008, Poisson Geometry in Mathematics and Phys- wicz was taken, but he was fortunate enough, or ics” at the École Polytechnique Fédérale, Lausanne, in July 2008. It was preceded by tributes to Stanisław daring enough, to escape. In those days, he did Zakrzewski, founder of the series of international con- what he could to help those who were in mortal ferences on Poisson geometry, who died in April 1998 danger, in particular Jewish colleagues.2 After the (by Alan Weinstein), to Paulette Libermann on the first Liberation, the University of Strasbourg returned anniversary of her death (by Charles-Michel Marle), and to Strasbourg. In 1949 he was named professor at to Moshé Flato, co-author and friend of Lichnerowicz, the University of Paris, and then in 1952 he was who died in November 1998 (by Daniel Sternheimer). This tribute was followed by the award of the “André 2In his autobiography [S 1997, p. 200], Laurent Schwartz Lichnerowicz Prize in Poisson Geometry” to two prominent wrote that one day Lichnerowicz contrived to be in a police young mathematicians. The October 2008 issue of the station and, while an officer was inattentive, he managed Gazette des Mathématiciens, in addition to carrying a to borrow a stamp and apply it to a false identity card French version of the present article, has an announce- which he, himself, did not need, but which could save the ment of the prize; an announcement also appeared in the life of a colleague or a student. To survive the war years in November 2008 Notices, page 1285. France with some honor was itself a great achievement.

244 Notices of the AMS Volume 56, Number 2 elected to a chair at the Collège de France, the most prestigious position in French higher education.3 When Lichnerowicz was elected to the Académie des Sciences de Paris—he was only 48, exceptionally young for a member of the Académie in those days—his students, as was customary, collected money to offer him his Academician’s sword. (The sword is the only part of the Academician’s very elaborate uniform that reflects his or her personality and accomplishments.) But two years later, for his fiftieth birthday, they contributed nearly as much to offer him something more to his taste, …a pipe! Indeed we could not imagine him without his pipe at any time …except during his lectures when he would fill the blackboard with equations in his dense handwriting, equations almost always com- prising many tensorial indices. It is a fact that he Archives. France de Collège the of courtesy Photograph can be seen in every photograph…with his pipe. André Lichnerowicz. Lichnerowicz’s work in general relativity began with his thesis, in which he gave the first global harmonic spinors [L 1963], in which he proved that, treatment of Einstein’s theory of general relativity for any spinor field, ψ, and determined necessary and sufficient condi- 1 ∆ψ ρ ψ Rψ , tions for a metric of hyperbolic signature on a = −∇ ∇ρ + 4 differentiable manifold to be a global solution for where ∆ P 2 is the Laplacian on spinors, the = the Einstein equations. He proved that there can- square of the Dirac operator P, is the covariant ∇ not exist any gravitational solitons; he established derivative, and R is the scalar curvature. And he the “Lichnerowicz equation”, an elliptic semi-linear continued working on spinors to his last days. equation used in the solution of the constraint At the beginning of the 1970s Lichnerowicz’s in- equations to be satisfied by the initial conditions terest turned to the geometric theory of dynamical for Einstein’s equations. He pursued this area of systems. Symplectic geometry had been studied for study throughout his research career. “Differential some time.4 In January 1973 a conference, “Geo- geometry and global analysis on manifolds”, “the metria simplettica e fisica matematica”, was held relations between mathematics and physics”, “the in Rome that was, I believe, the first international mathematical treatment of Einstein’s theory of meeting on this topic. As a young researcher I at- gravitation”, this is how he, himself, described his tended the congress, and heard and met many of main interests and achievement in the interview the founders of symplectic geometry among whom published in Hommes de Science [HdeS 1990]. were Jean Leray, Irving Segal, Bertram Kostant, His work in Riemannian geometry remains Shlomo Sternberg, Włodzimierz Tulczyjew, Jean- particularly important. He was among the first Marie Souriau as well as the young Alan Weinstein geometers to establish a relation between the and Jerry Marsden. And Lichnerowicz was one of spectrum of the Laplacian and the curvature of the organizers of the meeting and delivered the the metric; he proved the now classical equivalence opening lecture. of the various definitions of Kähler manifolds; he The main reason that we pay tribute to Lichnero- showed, together with Armand Borel, that the re- wicz’s memory here, today, at this conference on stricted holonomy group of a Riemannian manifold Poisson geometry, is that he founded it. This was is compact, and of course many other important a few years before the publication of the deforma- results. tion quantification paper I recalled at the beginning In the early 1960s Lichnerowicz established of this tribute. Cartan’s and Weyl’s theory of spinors in a rigorous His son, Jérôme Lichnerowicz, speaking of differential geometric framework, on a pseudo- his father’s collaboration with Moshé Flato, said: Riemannian manifold with a hyperbolic (Lorentzian) “There was no master and no student but an metric. Using this geometric approach in his incredible synergy between friends. I saw Moshé courses at the Collège de France in 1962–1964, encourage André when, ageing, he doubted his own he developed Dirac’s theory of the electron and strength,” and he added: “I heard Moshé tell me: 3 that of Rarita-Schwinger for spin 2, and then the ‘It is unbelievable, he [Lichnerowicz] had an arid Petiau-Duffin-Kemmer theory as well as the theory period, but now he is back doing mathematics as of the CPT transformations, while also in 1963 he 4 published the landmark Comptes rendus note on As Hermann Weyl explained at the beginning of Chapter VI of his book The Classical Groups [W 1939], he had 3A chair in mathematics was established by François I at coined the adjective “symplectic” after the Greek as an the founding of the Collège in 1531! alternative to the adjective “complex”.

February 2009 Notices of the AMS 245 before!’.” [CMF 2000] Starting in 1974, working his apartment on the Avenue Paul Appell, on the with Moshé Flato and Daniel Sternheimer, Lich- southern edge of Paris. Surrounded by collections nerowicz formulated the definition of a Poisson of journals and piles of papers, Lichné, with his manifold in terms of a bivector, i.e., the contravari- pipe, would offer encouragement and invaluable ant 2-tensor advocated by Lie, Carathéodory, and hints as to how to make progress on a difficult Tulczyjew, which is the counterpart of the 2-form research problem. I knew then, we all knew, that of symplectic geometry. In his article published in we were talking to a great mathematician. But I did Topics in Differential Geometry [L 1976] he defined not even guess that I was talking to the creator of a the canonical manifolds, and one can already find theory which would develop into a field in its own in that paper a formula for the bracket of 1-forms right, one with ramifications in a very large number associated to a Poisson bracket of functions, al- of areas of mathematics and physics. though still only for exact forms, References [df , dg] df , g. = { } [BBFLS 1978] François Bayen, Moshé Flato, Chris (Later he showed that the canonical manifolds Fronsdal, André Lichnerowicz, Daniel Stern- heimer, Deformation theory and quantization, An- are those Poisson manifolds whose symplectic nals of Physics 111 (1978); I. Deformations of sym- foliation is everywhere of co-dimension one.) In plectic structures, 61–110; II. Physical applications, his 1977 article in the Journal of Differential Ge- 111–151. ometry, “Les variétés de Poisson et leurs algèbres [L 1982] André Lichnerowicz, Choix d’œuvres mathé- de Lie associées” [L 1977], Lichnerowicz introduced matiques, Hermann, Paris, 1982. the cohomology operator that is now called the [PQG 1988] Physique quantique et géométrie, Colloque “Poisson cohomology operator” but really should Géométrie et Physique de 1986 en l’honneur de André be called the “Lichnerowicz-Poisson cohomology Lichnerowicz (Daniel Bernard and Yvonne Choquet- operator”, a profound discovery. We read there as Bruhat, eds.), Hermann, Paris, 1988. • Yvonne Choquet-Bruhat, L’œuvre de André well as in [BFFLS, 1978] that, in the particular case Lichnerowicz en relativité générale, pp. 1–10. of a symplectic manifold, • Marcel Berger, L’œuvre d’André Lichnerowicz en géométrie riemannienne, pp. 11–24. µ([G, A]) dµ(A), = • Charles-Michel Marle, L’œuvre d’André where A is a field of multivectors. (The notations Lichnerowicz en géométrie symplectique, pp. 25–42. are G for the Poisson bivector and µ for the pro- [HdeS 1990] Hommes de Science, 28 portraits, Entretiens longation to multivectors of the isomorphism et photographie de Marian Schmidt, Hermann, Paris, from the tangent bundle to the cotangent bundle 1990. [Gazette 1999] Gazette des Mathématiciens 81 (1999), defined by the symplectic form, the bracket is the 94–95, and 82 (1999), 90–108. Schouten-Nijenhuis bracket, and d is the de Rham [Notices 1999] Marcel Berger, Jean-Pierre Bourgui- differential.) This formula, which we rewrite in a gnon, Yvonne Choquet-Bruhat, Charles-Michel more familiar notation, Marle, and André Revuz, André Lichnerowicz (1915–1998), Notices Amer. Math. Soc. 46(11) (1999), ω([π, A]) d(ω(A)) or π(dα) d (πα) = = π 1387–1396. (here G is replaced by π, and µ by ω, with inverse [S 1997] Laurent Schwartz, Un Mathématicien aux Prises avec le Siècle, Odile Jacob, Paris, 1997. π, while α is a differential form and d is the π [L 1963] André Lichnerowicz, Spineurs harmoniques, Lichnerowicz-Poisson differential, d [π , ], π = · C. R. Acad. Sci. Paris 257 (1963), 7–9. acting on multivectors) is the precursor of the [W 1939] Hermann Weyl, The Classical Groups, Prince- chain map property of the Poisson map, map- ton University Press, Princeton, NJ, 1939; second ping the de Rham complex to the Lichnerowicz- edition, 1946. Poisson complex, and, more generally, this article [CMF 2000] Jérôme Lichnerowicz, in Conférence Moshé is the point of departure for the great develop- Flato 1999, vol. I (Giuseppe Dito and Daniel Stern- ment of Poisson geometry that we have witnessed heimer, eds.), Kluwer, Dordrecht, 2000, pp. 7–8. and in which we are participating here. Together [L 1976] André Lichnerowicz, Variétés symplectiques, with his earlier articles written jointly with Flato variétés canoniques et systèmes dynamiques, in Top- ics in Differential Geometry, in memory of E. T. Davies, and Sternheimer [FLS 1974, 1975, 1976] and with Academic Press, New York, 1976, pp. 57–85. the article in the Annals of Physics [BBFLS 1978], [L 1977] ——— , Les variétés de Poisson et leurs algèbres solving quantization problems by a deformation de Lie associées, J. Differential Geometry 12 (1977), of the commutative multiplication of the classical 253–300. observables when given a Poisson structure, this [FLS 1974] Moshé Flato, André Lichnerowicz, article established the foundation of what has be- Daniel Sternheimer, Déformations 1-différentiables come a vast field of mathematical research. d’algèbres de Lie attachées à une variété symplectique It was a privilege for Lichnerowicz’s many doc- ou de contact, C. R. Acad. Sci. Paris Sér. A 279 (1974), toral students, of whom I was one in the late 1960s, 877–881. to be received by him in his small office under the roof of the Collège de France, or in the study of

246 Notices of the AMS Volume 56, Number 2 Presidential Views: Interview with James Glimm

Every other year, when a new AMS president takes office, the Notices publishes interviews with the outgoing and incoming presidents. What follows is an edited version of an interview with James G. Glimm, whose two-year term as president ends on January 31, 2009. The interview was conducted in fall 2008 by Notices senior writer and deputy editor Allyn Jackson. Glimm is a Distinguished Professor of Applied Mathematics and Statistics at Stony Brook University. An interview with president-elect George Andrews is scheduled to appear in the March 2009 issue of the Notices.

Notices: As AMS president, you have attended Glimm: Certainly for several many meetings and talked to many mathemati- centuries, mathematics, in its ap- cians. What kinds of issues or challenges did you plications, has been dominated hear about in these conversations? by following in the footsteps of Glimm: Of course, the math community is quite physics: taking equations from the diverse, and the challenges are reflected by the physical sciences, figuring out what diversity of the community. There are concerns could be said about the solution about getting bright students into majors, because spaces, finding numerical methods many of them are placing out of calculus courses, for evaluating solutions, making which is a traditional way of recruiting students. estimates and approximations, tak- They take calculus in high school instead. There is ing asymptotic limits. There are all a set of pedagogical issues of that type. In terms of sorts of ways that a mathematician research, I think there is the usual concern about can extract information related to the poor level of funding in mathematics. a set of equations. Going forward, James Glimm I actually would turn the question around a little that process is maturing, and some bit and argue that there is a lot of vitality in the of the more innovative develop- math community. I think there are many positive ments are in the past. If you look into the future, things going on. there will be a big emphasis on doing the same thing, where the input is not the laws of physics Notices: Can you give some examples? but observed data. Just as there was an explosion Glimm: Intellectually, the triumph with the of computer knowledge that allowed the solution Poincaré conjecture is certainly something that of equations in physics, there is an explosion of we are all delighted about. The continued prog- sensor data that allows meaningful analysis of ress in the connections between geometry and experimental facts independently of any laws of string theory always seems to be very surprising. physics. Sometimes there isn’t even the prospect The continued blossoming of new applications of an intermediate law of physics, for example, if requiring new types of mathematics is always you are doing pattern recognition of photographs very heartening. Sometimes the math community in a newspaper or something like that. Sometimes thinks they’ve missed the boat. People say, “That people run conservation laws to sharpen up already happened twenty years ago and now it’s boundaries in images, but basically the problem too late.” But there are always new opportunities is not directly connected to physical equations and new chances. in any obvious way. The modeling is pretty much Notices: One of these new areas of opportunity independent of the equations. was the subject of a special session you organized at the 2008 Joint Mathematics Meetings called “Math- Notices: So this area offers new ways for mathematics of Knowledge and Information”, and you ematicians to contribute? will organize another special session on this topic at Glimm: Absolutely. If you think that we have the January 2009 meetings. Can you describe what had several centuries squeezing juice out of the this field is about and why it is important? equations of physics, we might have some number

February 2009 Notices of the AMS 247 of centuries with data. I think it’s a big issue. It’s or of automatically translating between languages, a century-long issue. that are based on computer models that solve Mar- Notices: Are scientists clamoring for mathemati- kov processes. There is something called a hidden cians’ help with this? Markov model that drives the statistics of language Glimm: Yes, in part, and partly they just do it recognition and of speech recognition. without us. But that is no reason for us to stand One of the themes that I have been pushing, back and not join in. If we do stand back, we will especially for AMS meetings, is what I call the “big find that other people will step forward, and we tent” philosophy of mathematics. This has several will once again find our subject diminished by aspects. One is that lively areas that happen to be having lost a very vital component. It was for this somewhat at the fringe of whatever people think reason that I thought this was a strategic choice the center is, should not be competing against to emphasize this particular application. It has things in the center. They both have their own nothing to do with my own research, so I have no validity. Neither should compete against the other, personal interest in it. I just believe that it has a but each one should compete against some abso- huge role in the future of mathematics. lute standard of what we want in our meetings. In Notices: Can you give examples of work in this the big tent philosophy, the way the tent gets big area? is by emphasizing the edges. It has to be done by Glimm: The topics in the special session were enlarging the space, so that includes enlarging the very diverse. One talk was about trying to under- meetings. I have been continually urging the AMS stand the traffic patterns in the Internet. Financial to enlarge its meetings. Now, that can’t be done mathematics wasn’t included in the session but instantly because there are long-term contracts might well have been, and that is another example. and meetings are planned out years in advance. It’s People use this method for analyzing genome data, a little bit like trying to steer a battleship. But you medical data, and protein expression data. The can always change the direction, achieve incremen- biomedical world is part of this explosion of data. tal progress, and move towards something that For instance, even in structural biology, when you will reach these goals over some period of years. are trying to predict a protein, there are two basic In the Washington meeting I think the “big tent” approaches. One is based on solving the classical spirit has been reflected in the program. equations of physics for the interaction of atoms Notices: You also have been interested in under- that lead to the formation of molecules. But you graduate education during your time as president. can just as well do it by pattern recognition, where Can you tell me about this? you look at different bonds between the proteins Glimm: We have a particular project that I and how they attach. They attach first of all on a think is probably going to be promising, to look linear chain, and then they have to fold up in cer- into computer grading of homework. Now, the tain characteristic patterns. There is a wealth of practices for grading of homework are all over the data about the geometry of proteins whose struc- map. Sometimes homework is graded assiduously, ture has been solved. It’s like a library of solutions. sometimes it is not graded at all, sometimes it is You look through this library and pick a solution graded by an undergraduate who didn’t take much that is very similar to your current problem or care, sometimes it is graded but returned two little piece of a current problem, and you figure weeks later. On the average, there is a lot of room out that a certain bond is likely to fold in a certain for improvement. way. That’s basically pattern recognition. There are Computer-graded homework captures the stu- many cases in biomedical research where there are dents’ attention. Apparently the students get ex- laws of physics that apply, but it is more efficient cited about homework and spend more time on it and effective to solve problems on the level of because they get instant feedback. It’s somewhat pattern recognition. The same happens in weather like a computer game. So they just sit there and do forecasting. Global weather forecasts are achieved it until they have mastered it, and of course that’s by solving differential equations numerically. For the way to learn. The problems are generated with local weather forecasting, usually they see what random input, which discourages copying. The ex- the global forecast says is coming in and then look perience is that, with computer-graded homework, up the local history and find an event that most we probably have the same number of Ds and Fs closely matches the regional part of the global that we always had, but some of the Cs have moved forecast. They look up weather for those days and up to Bs and some of the Bs have moved up to As. get a range of what could happen as the forecast. The overall effect is roughly a grade point aver- So it’s basically pattern recognition. age in the scoring. That’s what the rumor circuit Notices: So this really goes across all areas of says, and we are proposing to have a more careful science. evaluation and to discover the “lessons learned”. Glimm: Absolutely, all of science, but also areas We will find out what people have to say when they that were not previously considered to be science. For have used computer grading—whether they kept it, instance, there are ways of recognizing handwriting, whether they didn’t keep it, and why. Also, we will

248 Notices of the AMS Volume 56, Number 2 find out practical things, like what is needed for in an evaluation stage, different people will decide infrastructure, for computer resources or human to do different things. Eventually the community resources, to run it. We will make this informa- will more or less make a collective decision and tion available to the math community. If you are a cluster around some set of technologies that are freshman taking precalculus or calculus, what is beneficial. the chance you would be in such a course? I would Notices: Is there anything else you wanted to guess it would be in the single digits of percent- mention? ages. But I think it is ready to jump, to 20 percent, Glimm: One thing I would like to note, with plea- then 40 percent, maybe 60 percent. At that point it sure, is the fact that there are private donors for would be freestanding, and people would do what mathematics. I don’t recall this at other points in they judge worthwhile with it. my professional lifetime. We have a new privately Notices: What would be the AMS role in this? funded institute at Stony Brook [the Simons Center Glimm: The AMS has a very important role to for Geometry and Physics; see Notices, June/July play in issues relating to education of undergradu- 2008, page 685–686]. There is the American Insti- ates. Obviously, MAA will be in the lead for many tute of Mathematics in Palo Alto, which is also pri- aspects of these issues, but the AMS retains an vately funded. There have been private donations important role. The faculty at research universi- to the Mathematical Sciences Research Institute in ties are responsible for the education of a very Berkeley. Another example is the Clay Mathemat- significant number of freshman and sophomores. ics Institute. We have been more successful with Many of these faculty look primarily to the AMS private donors than at any time I can recall in my for leadership. Generally, the faculty who teach professional lifetime. effectively enjoy their teaching greatly, and so the Notices: Why do you think that is? rewards of good teaching are rather obvious. We Glimm: Well, I don’t have an answer to that. want to promote ways to help bring this about, Maybe some mathematicians have gone into the and, particularly for faculty at research universi- private sector and become wealthy. I don’t have a ties, we want to do this without compromising the complete list of these things, but it seems to me quality of their research. The computer grading to be a huge explosion compared to what used to of homework seems to be the type of low-hanging be the case. Notices: What did you enjoy most about being fruit that is ideally suited to this situation. president? We have applied for a grant from the National Glimm: I’ve watched the math community over Science Foundation—to the Division of Undergrad- many years wring its hands over the “spilled milk” uate Education, so the grant would not compete decisions of the past. There is no way to recover with research grants in the Division of Mathemati- the past, but these decisions are being made all cal Sciences. We proposed that the AMS do the kind the time. Boundaries between subjects look very of study I just indicated. So that is one role. I have obvious when you are at the center of the subject been pushing this through my office as president looking out into the distance, where there is some in any forum where I have a chance to make such boundary seemingly off at infinity. But when you statements. I think I have raised consciousness go out to the boundary, these areas are very lively. about these issues. Some of the products belong We can take actions to promote mathematics and to MAA [Mathematical Association of America], not repeat actions that will make people complain and some belong to commercial publishers. I don’t twenty years from now about decisions made at think there is any need for a new product, and there the present time. is no reason for the AMS to have its own product The Society seems to me to be a particularly competing with others. I think if we just encourage well-run organization. I don’t want to say it runs on our members to use one of these products, they auto-pilot, but there is a structure for how things can take their pick. So the real role is to facilitate are done, and the structure seems to suit people a climate whereby people will evaluate computer and leads naturally to decisions that are construc- homework-grading systems and presumably come tive. I had a few more committee meetings than to use them. If the systems work as promised, then I would normally have volunteered for, but that there will be an uptick in the quality of education goes with the game. You can’t do this kind of thing and the satisfaction of students. without being immersed in the committees. Notices: Many people are using clickers in mathematics classrooms. We will have an article on this topic in the Notices [the article appears in this issue]. Glimm: There is a certain amount of ferment about these different technology tools. I’m not trying to advocate any particular one of them. I just think that we can make some progress by adopting some of these tools. While the tools are

February 2009 Notices of the AMS 249 Ask Professor Nescio

Editor’s Note: Graduate students, early career faculty, and other mathematicians may have professional questions that they are reluctant to pose to colleagues, junior or senior. The Notices advice column, “Ask Professor Nescio”, is a place to address such queries. Nomen Nescio is the pseudonym of a distinguished mathematician with wide experience in mathematics teaching, research, and service. Letters to Professor Nescio are redacted to eliminate any details that might identify the questioner. They are also edited, in some cases, to recast questions to be of more general interest and so that all questions are first person. Some letters may be edited composites of several submitted questions. Query letters should be sent to [email protected] with the phrase “A question for Professor Nescio” in the subject line. —Andy Magid

Dear Professor Nescio, but even those who heed this sage advice often fail I got my Ph.D. as a good graduate student at because the task is so challenging. a respectable university. Yet I find 80–90% of the With time you will probably discover that you articles and reviews in the Bulletin that the AMS comprehend more, provided the term “compre- sends me to be simply incomprehensible; within hend” is suitably understood. If you seek complete a page or two, sometimes already from the first mastery, forget it; things will never get better. If sentence on, it might as well be Slovenian. I don’t you seek, however, to place the subject matter in know what those words mean. Am I an idiot? Do some context, to get a general idea what is happen- other people have the same trouble? What can or ing in the given specialty, to see where some area is should I do to increase my comprehension? headed, then you will get some satisfaction. Trying —Sincerely to increase the breadth of your view of mathemat- R. H. ics is a worthy undertaking. It is also fun. So many of my colleagues narrow their view so that it barely Dear R. H., escapes their immediate research. Professor Nescio If I am doing the mathematics correctly, this frequently bemoans this lack of peripheral vision. means you understand 10–20% of the items in the So I salute your desire and wish you well. Bulletin. Congratulations! You are better educated —Respectfully, Professor Nescio than Professor Nescio. I try to read many abstracts from areas close to Dear Professor Nescio, my research interests and often even that proves I have published a joint paper with another daunting. The plain fact is that mathematics is author, and the reviewer of Math Reviews wrote in highly specialized. That’s something you probably her review in MathSciNet that we had to mention already knew, but what you are finding out is that her book in the paper. Since her book has no con- it is even more specialized than you had previously nection at all with our paper (and with the field in thought. Be assured this lack of comprehension is which our paper belongs), there is no other expla- not your fault. It is not the “fault” of mathematics nation than that she wrote her review in that way either. It is just a fact of life. We can lament the just to increase her citation index in MathSciNet specialization of mathematics and wish that things or to sell her book or both. As soon as I saw that were different, but that is nonsense. The special- review in MathSciNet I wrote to her and to Math Re- ization is just part of the nature of the subject and views as well but the problem has not been solved a requirement for its development. yet. That review should not remain in MathSciNet The late Paul Halmos advised colloquium speak- as it is. Could you please help me to solve that ers to make the first 15 minutes of their talks ac- problem? Thanking you for your time, cessible to the entire audience. Do you know how —Sincerely yours, difficult that is? Surely if you have attended many Professor N. K. colloquia (and as someone who tries to read Bul- Dear Professor N. K., letin articles, I am assuming you wish to be widely This is a rather irritating situation. I am afraid, informed of mathematics and are therefore a however, that Professor Nescio’s powers are quite faithful attendee at your department’s colloquia), limited. I certainly have no influence over Math- you have seen how miserably most speakers fail SciNet. I do have some appreciation of the fact that to do this. Many, for whatever reason, do not try; the MR editors have no desire or inclination to act

250 Notices of the AMS Volume 56, Number 2 as a referee in such matters as deciding whether senior faculty on research and ripen their talents. you or the reviewer has the most legitimate case. The benefit for the host is that there is a constant For one thing they have only enough staff to do infusion of “young blood” into the intellectual life their normal work. (And perhaps you will not of the department. object if I say at this juncture that MathSciNet The time spent in graduate school is not suffi- is one of the greatest applications of computers cient to fully launch a robust research career. The and human intelligence to help us in our work.) intellectual growth of a postdoc can be enormous. To enter into a dispute like this would consume After two or more years under the supervision of a enormous amounts of their time since, as I am sure thesis adviser, it helps to be exposed to a new view- you can appreciate, they cannot merely accept your point and a different current to propel you into word that the reference is irrelevant. that vast open sea of mathematical research. This Professor Nescio’s interest in human nature is is also a good reason for attending conferences and as great as his interest in mathematics, but un- speaking about your research, but there is more like in mathematics he often sees things that are intensity in the postdoctoral experience and it lasts so disheartening. Why someone, presumably an for a longer time. With a reduced teaching load and, established mathematician who is asked to write presumably, less service activity on committees, reviews, would want such a small aggrandizement there is also ample time to pursue research and and be willing to pay the coinage of public intellec- benefit from this intensity. This type of benefit also tual dishonesty is perplexing. Could it be that some accrues to the more senior host; we all benefit from egos are so great that they actually believe such discussion and input about our ideas. statements? Perhaps such a question is exactly I think you can see that if this is what happens, what is so fascinating about the study of people. what the position is called is of little importance. Unfortunately the incident that personally af- Whether you are called an instructor, lecturer, or fects you is not the first such example that Profes- assistant professor has no relevance. Below I’ll talk sor Nescio has heard about. You might take a bit a bit more about the title when I discuss abuse. of satisfaction that the aficionados in your area If you have a successful postdoc experience, this will recognize the irrelevance of her comment and will help you obtain a position at a research depart- reach the same critical judgment that you did. ment. In fact, few such departments hire tenure- —Respectfully, track faculty straight from graduate school. If you Professor Nescio are on a search committee and examine a batch of applications for an assistant professorship, when Dear Professor Nescio, you place the folder of a fresh Ph.D. next to that I’ve been asking several mathematicians and of someone in the third year of a postdoc, the other non-math academic friends what their per- difference is enormous. The postdoc has more ception is of the concept of “postdoc”. achievements, and there are fewer questions about What is the purpose of a postdoc? Why would their personal contribution to their research. The a recent Ph.D. (or soon-to-be-graduating Ph.D.) letters of recommendation are usually stronger, want to take a postdoc? Does completing a postdoc with heavier discussions about accomplishment improve one’s chances for a “better job”? What’s rather than promise. If your ambition is to teach at the role of the host institution—are they providing a four-year institution, however, taking a postdoc some sort of benefit to the postdoc that a person has less merit. It can still benefit you but I suspect taking a tenure-track position would not normally in most cases it will not make you a more attrac- get? How does a postdoc position differ from a tive candidate. “Visiting Assistant Professor” position? Thanks. You said you consulted academics outside —Confused about academic paths for mathematics. Be aware that postdoc positions in mathematicians the physical and biological sciences have been around longer than in mathematics and there are Dear Confused, far more of them. There are some enormous dif- I love this question. It will give Professor Nescio ferences: In these sciences, postdocs last much a chance to discuss a topic that he frequently and longer and there are usually no teaching duties. usually enjoys but that also occasionally reveals The experimental sciences depend on postdocs abuse of language, young mathematicians, and and graduate students to staff laboratories. the profession. Now for the abuse, which can take many forms Here is what I think a postdoc means (or should but usually occurs when the institution wants mean) and is associated with the term by most pro- cheap, temporary teaching power or when the fessional mathematicians: a temporary position for “postdoc” lasts only a year. Some institutions at new or almost new Ph.D.’s that lasts two or three least have the decency to give these positions a years and carries a reduced teaching load of two different name such as Visiting Assistant Profes- or three courses per academic year. The idea is sor or Teaching Postdoc. In my opinion this is not that the postdoc has a chance to work with more a good way for a young person to launch a career.

February 2009 Notices of the AMS 251 I have seen such positions with a teaching load of three courses per semester. What sort of extra training and education you are supposed to get from teaching a lot of courses escapes me. Where is the valued-added? If the appointment is for only a year, you will begin applying for another position almost as soon as you enter the campus. If a postdoc is never allowed to teach an advanced course, that’s abuse. If he/she teaches a large class with no grading or GTA assistance, that’s abuse. The purpose of a postdoc is not to make life easier for faculty at the host department. (Professor Nescio must approach this topic gingerly; he is getting very upset.) Accept such a job only if you must. When you leave such a position after a few years, you are no longer a new Ph.D. and for the extra time you will have little to add to your CV. You may look less attractive to employers. What is the role of the host institution? Let’s first ask what it should be, which is to help you launch your career. This means providing you with some travel money, allowing you to teach some advanced courses, ideally including a seminar in your area, and mentoring you into the next phase of your career. Should you ever interview for such a position, ask about the teaching. Can you teach a seminar? (There is nothing like teaching a graduate seminar to give you perspective and discover research problems.) Will you have a paper grader for the elementary courses, especially the larger classes? Will they give you the option of doing more teaching one semester for less the next? What should you do while a postdoc? Of course A m e r i c A n m AthemAticAl S o c i e t y you should pour yourself into your research. Go view ams catalogs online! to conferences, talk about your research whenever you can, make as many contacts as possible. Take The links within each title description will bring you your teaching seriously. Professor Nescio would be to an area with greater details, table of contents, and most disappointed to hear that a postdoc did oth- other supplementary material. erwise as this would abuse the students, abuse the profession, and reflect badly on you when you enter the job market. You might also search for a tenure- track job in a highly selective way. From the start, keep your eye open for very attractive positions and apply for them. Discuss this with your host before doing it (and I am not talking about sending out a hundred applications or even a dozen). But if a very appealing position becomes available, you should try for it. It is unlikely to be available when your postdoc ends; and you can enter the search without the pressure of having to find a job but actually looking for an opportunity. Several things were unclear from your letter, for example whether you are a student, whether you are personally trying to decide whether to apply for a postdoc, etc. I hope that whatever the case, www.ams.org/bookstore/newpubcatalogs Professor Nescio has provided some information you will find useful. Whatever your status, he wishes you the best of good fortune. —Respectfully, Professor Nescio

252 Notices of the AMS Volume 56, Number 2 A Clicker Approach to Teaching Calculus

Martina Bode, Denise Drane, Yifat Ben-David Kolikant, and Mary Schuller

Clickers (electronic voting systems) are all the for two-way communi- buzz in higher education these days as many cation (generally radio universities and colleges invest significant sums frequency) between an of money to integrate these systems into their instructor and a group of classrooms. But what are clickers? Are they just students. In classrooms another high-tech gimmick, or can they really be with clickers, instructors used to improve learning? Can clickers be used can pose questions dur- efficiently in calculus classes? ing class, usually on a In an ideal world, students would take calculus PowerPoint slide, and for the sheer love of it. The reality is, however, the students respond that calculus is a service course, and most stu- anonymously using the dents take it to fulfill university requirements. keypad on their click- Engaging students in calculus classes thus can be ers. Responses to the a challenge. Furthermore, in traditional lectures, question can then be dis- students passively take notes, at times barely pro- played on a screen so both students and the cessing the material as they struggle to keep their instructor can see the Figure 1. Clicker attention focused for an hour. Students often fear percentage of the class device. that they are alone in not understanding the ma- that chose each response. Questions can range terial and are at times afraid of asking questions from multiple-choice, true/false, matching items, in class. At the end of class, both students and and ranking items, to numerical and short text instructor may leave without knowing whether the answers. Clickers can be used in a variety of ways, material has been understood. from checking conceptual understanding, testing Clickers can be used to address these chal- skills, provoking discussion, all the way to teach- lenges. The term “clickers” refers to the stu- ing and motivating new material. The benefits are dent input devices (see Figure 1) of elec- manyfold: tronic voting systems. These systems allow (1) Instructors receive instant feedback on the students’ comprehension and misconcep- Martina Bode is senior lecturer of mathematics at North- tions. western University. Her email address is m-bode@ northwestern.edu. (2) Students receive instant feedback regarding their understanding and how they Denise Drane is associate director, Research and Eval- compare to the rest of the class. uation, at the Searle Center for Teaching Excellence, Northwestern University. Her email address is d-drane@ (3) Students are more focused and are actively northwestern.edu. engaged in learning during class time. Yifat Ben-David Kolikant is at the School of Education, He- To encourage peer-to-peer interactions, a click- brew University, Jerusalem. His email address is er can be assigned to a group of students who [email protected]. must discuss their answer before responding to the Mary Schuller is manager, surgical education, at North- question. In our experience, the small group setting western Memorial Hospital. Her email address is provides a more intimate and non-threatening en- [email protected]. vironment for students to admit difficulties with

February 2009 Notices of the AMS 253 the material. Students are also more willing to with a speed of 18 ft/s. At what rate is the distance divulge their answers in class since they are rep- from second base decreasing when he is halfway to resenting the group’s work rather than the work first base? of just one individual. How can clickers be used in calculus class- Although this is a great standard calculus text- es to enhance learning? What type of questions book problem ([1]) to ask on a quiz or test, this are good clicker questions? First of all, clicker questions can be used in different contexts; be- problem might be too complex to ask in the middle fore, during, or after introducing new concepts. of class using clickers. However, a problem of this The sample questions below are simple, basic type can be divided into several parts as follows. questions with the goal of engaging students in (i) Students are asked to draw a picture mod- discussion and learning. In parentheses are the eling the situation. With their clickers stu- percentages of students at Northwestern Universi- ty in single variable calculus classes, 2006-07, who dents indicate: chose each response. All questions were asked (a) done drawing the picture prior to introducing or reviewing the concepts (b) more time needed required to answer these questions. Students dis- Students click when they have complet- cussed their answers in small groups of two to six ed the task, and in their groups, select a students before responding with the clickers. student to put the picture on the classroom Example 1. A discussion starter board. True or False? arcsin(sin π) = π (True 50%, False 50%) (ii) The next PowerPoint slide includes a picture modeling the situation where x is the Example 2. A misconception check distance from the runner to first base, and True or False? If f has a local maximum or min- z the distance from the runner to sec- ′ imum at x = c, then f (c) = 0. ond base. Then students are asked what (True 89%, False 11 %) quantity this question is asking to find: ′ ′ Example 3. A basic concept check question (a) x (t), (b) z (t), (c) None of the above, Suppose you know that a differentiable function (d) I don’t know ′ ′′ f has f (3) = 0, and f (3) = 4. Which of the fol- (iii) The last part of this problem can then lowing statements must be true? be posed as a multiple choice question = (a) f has a local maximum at x 3 (16%) to evaluate z′(t), or, with more advanced (b) f has a local minimum at x = 3 (32%) clickers, students can enter the correct (c) f has a point of inflection at x = 3 (42%) quantity for z′(t). (d) None of the above (10%) The purpose of this question was to help stu- All textbooks have great questions that can dents discover the second derivative test on their be modified to use with clickers. Some books, own. in addition, contain conceptual questions specif- Example 4. A series of true/false questions ically designed to use with clickers, for example ConcepTests ([2], [3], [4]). (1) If limn→∞ an = 0, does that imply that P∞ a converges? What do students think about clickers, and n=a n P ∞ what is the evidence for better learning in class- (2) Conversely if n=a an converges, does that imply that lim →∞ a = 0? rooms with clickers? The following tables present P n n ∞ survey data from 348 students in six different (3) If n=a an diverges, does that imply that limn→∞ an ≠ 0? calculus classes taught by the same instructor at Northwestern University, 2005–2008. (4) If limn→∞ an ≠ 0, does that imply that P∞ n=a an diverges? Conceptual Understanding These questions were posed with the intent to lead students to discovery of the divergence test. [Q1] I am more aware of my misunderstand- While only 49% chose the correct answer for (1), ings/difficulties than in traditional classes. by the time question (4) was posed, 81% chose the [Q2] Using the clickers helps me to understand correct answer. the concepts behind problems. Example 5. A multi-step problem [Q3] The questions asked during clicker ses- A baseball diamond is a square with sides of 90 sions help me to understand what is expected ft. A batter hits the ball and runs towards first base from me in this class.

254 Notices of the AMS Volume 56, Number 2 [Q13] Collaborative work among group mem-

Conceptual Understanding bers contributed to a better quality solution to the problems.

70.1

Q1 15.8

14.1 Interaction and Discussion

48.4

14.9

32.6

Q2 Q8 25.3

19.1

59.8

76.1

73.6

14.7 Q3 16.7

9.1

9.7

0% 20% 40% 100% 60% 80%

83.0

Agree Neutral Disagree 7.5 Q10

9.5

Learning 79.3

12.7 [Q4] Using clickers helps the teacher to become Q11 7.8 more aware of student diﬃculties with the subject matter. 80.5

13.0 [Q5] I have to think more in classes with clickers Q12 than in traditional lecture classes. 6.4 [Q6] Hearing other students explain problems 79.2

in their own words when working in our small 12.3 Q13 groups helps me to learn. 8.4 [Q7] I remember less after a class with clickers

0% 20% 40% 100% than after other classes. 60% 80%

Agree Neutral Disagree

Learning

Enjoyment

84.8

Q4 8.7 [Q14] Using the clickers helps me enjoy this 6.4 class more than I enjoy traditional lecture classes. [Q15] Seeing the class responses to a concept 70.0

18.7 question (histogram) helps increase my conﬁ- Q5

11.2 dence. [Q16] The clicker approach should be used for

75.2

14.4 other subjects. Q6

10.3 [Q17] I am more likely to attend class because of using the clicker system.

9.2

24.2 Q7

Enjoyment 66.5

0% 20% 40% 100% 60% 80%

79.0

Agree 13.0 Neutral Disagree Q14

8.1

Interaction and Discussion 57.8 28.6

Q15

[Q8] I got to know fewer students than I usually 13.6 do in a traditional class.

69.4 [Q9] I think that anonymous participation is a 16.8 Q16

good idea. 13.8 [Q10] I am more actively involved during classes with clickers than during traditional classes. 44.3

34.8 [Q11] Discussing clicker questions with other Q17 students in the class helps me to understand 20.8

0% 20% 40% 100% better the subject matter. 60% 80%

Agree [Q12] Team members were actively involved in Neutral Disagree solving the questions.

February 2009 Notices of the AMS 255 In the surveys at Northwestern, and several oth- [3] D. Hughes Hallett, M. Robinson, and D. Lomen, er published studies ([5], [6], [7]), students believed ConcepTests: Active Learning in Calculus, Mathe- that the use of clickers made them more aware matics Education into the 21st Century Project, Universiti Teknologi Malaysia, 2005. of their misunderstandings and helped them to [4] S. Pilzer, Peer instruction in physics and mathemat- understand what is expected in class. They al- ics, PRIMUS 11 (2001), 185–192. so felt that they were more involved in classes [5] J. Boyle and D. Nicol, Using classroom com- using clickers than traditional classes. Moreover, munication systems to support interaction and discussion with other students helped students to discussion in large class settings, Association of understand and learn the material. Finally, they Learning and Technology Journal 11 (2003), 43–57. [6] S. Draper and M. Brown, Increasing interactivity in reported that clickers made class more enjoyable. lectures using an electronic voting system, Journal Another advantage from the instructor’s perspec- of Computer Assisted Learning 20 (2004), 81–94. tive is that students are more eager to participate in [7] C. Elliot, Using a personal response system “follow up” class-wide discussions after engaging in economics teaching, International Review of in peer-to-peer discussions. Economics Education (online), (2003). Available Several studies have found increased inter- at http://www.economicsnetwork.ac.uk/iree/ i1/elliott.htm; accessed June 12, 2008. est, motivation, and retention in classes that use [8] J. E. Caldwell, Clickers in the large classroom: Cur- clickers ([7], [8]). Harvard physicist Eric Mazur rent research and best-practice tips, Life Sciences compared learning gains in his classes with and Education 6 (2007), 9–20. without clickers. In clicker-classes, students dis- [9] C. Crouch and E. Mazur, Peer instruction: Ten cussed their answers with their neighbors before years of experience and results, American Journal and after responding to clicker questions. Mazur of Physics 69 (2001), 970–977. [10] N. Lasry, Clickers or flashcards: Is there real- found that physics students within the clicker ly a difference?, The Physics Teacher 46 (2008), setting made larger gains on standardized physics 242–244. tests than the control group without clickers [9]. A recent study by Lasry [10] found students who used flashcards to respond made gains equal to those made by students using clickers. This suggests that it is not the technology itself that is responsible for gains in learning but the peda- gogy of engaging students during class, requiring them to engage in peer-to-peer discussion before responding with the clicker, and giving them immediate feedback. The use of clickers is not without its limitations. Mid-range clickers generally cost between US$20–US$60 per unit. As with all technology, trouble shooting problems can be frustrating and time-consuming. For instructors, additional class planning time is needed for preparing the questions and technology. Some instructors feel that the class time spent on clicker questions reduces the amount of time available to cover additional content. In our experience, the depth of student engagement with the content compensates for the reduced time to cover a wider breadth of material. Despite the drawbacks, we feel the advantages of using the technology outweigh the disadvantages. Although clickers may not make students fall in love with calculus, they may help them to be more engaged in calculus classes, which in turn may enhance learning.

References [1] J. Stewart, Essential Calculus, Early Transcenden- tals, Thomson, 2007, page 131, exercise 16. [2] The Calculus Consortium, Applied Calculus: ConcepTests, Wiley, 2006.

256 Notices of the AMS Volume 56, Number 2 2008 Annual Survey of the Mathematical Sciences (First Report)

Preliminary Report on the 2007–2008 New Doctoral Recipients

Polly Phipps, James W. Maxwell, and Colleen Rose

The preliminary report of the 2008 Annual Survey gives Preliminary Report on the a broad picture of 2007–08 new doctoral recipients from U.S. departments in the mathematical sciences, including 2007–2008 New Doctoral their employment status in fall 2008. This report is based on information collected from a questionnaire distributed to Recipients departments in April 2008. A follow-up questionnaire was This report presents a statistical profile distributed to the individual new doctoral recipients in October of recipients of doctoral degrees awarded by 2008. This questionnaire will be used to update and revise departments in the mathematical sciences at results in this report, which are based on information from the universities in the United States during the period departments that produced the new doctorates. Those results July 1, 2007, through June 30, 2008. All information will be published in the Second Report of the 2008 Annual Survey in the report was provided over the summer and in the August 2009 issue of the Notices of the AMS. The Faculty early fall of 2008 by the departments that awarded Salary Survey report, traditionally published as part of this report, the degrees. The report includes a preliminary will appear in the March issue of Notices of the AMS. analysis of the fall 2008 employment plans of 2007– Another questionnaire concerned with data on fall 2008 2008 doctoral recipients and a demographic profile course enrollments, graduate students, and departmental faculty summarizing characteristics of citizenship status, was distributed to departments in September 2008. Results this is an from this questionnaire will appear in the Third Report of the sex, and racial/ethnicexample group. This of preliminary a 2008 Annual Survey in the November 2009 issue of the Notices Table 1: Number of Departments Responding of the AMS. to Doctorates Granted Survey The Annual Survey series begun in 1957 by the American pull quote Mathematical Society is currently under the direction of the Data Group I (Pu) 20 of 25 including 0 with no degrees Committee, a joint committee of the American Mathematical Group I (Pr) 22 of 23 including 0 with no degrees Society, the American Statistical Association, the Institute of Mathematical Statistics, the Mathematical Association of America, Group II 52 of 56 including 2 with no degrees and the Society of Industrial and Applied Mathematics. The Group III 61 of 75 including 11 with no degrees current members of this committee are Richard Cleary, Richard Group IV 60 of 89 including 4 with no degrees M. Dudley, John W. Hagood, Abbe H. Herzig, Ellen Kirkman, David J. Lutzer, Joanna Mitro, James W. Maxwell (ex officio), Bart Ng, Group Va 19 of 21 including 1 with no degrees Polly Phipps (chair), Douglas Ravanel, Jianguo (Tony) Sun, and See “Definitions of the Groups“ on page 267. Marie Vitulli. The committee is assisted by AMS survey analyst Colleen A. Rose. Comments or suggestions regarding this Survey report will be updated in the Second Report of the Report may be directed to the committee. 2008 Annual Survey to reflect subsequent reports of additional 2007-2008 doctoral recipients from the departments that did not respond in time for this report. No adjustments have been made to the Polly Phipps is a senior research statistician with the Bureau of Labor Statistics. James W. Maxwell is AMS associate executive director for special numbers in this report for these departments. The projects. Colleen A. Rose is AMS survey analyst. Second Report, to appear in the August 2009 issue of Notices, will also reflect additional information

Fe b r u a r y 2009 No t i c e s o f t h e AMS 257 2008 Annual Survey of the Mathematical Sciences in the U.S. provided by the new doctoral recipients themselves, Highlights including their starting salaries. Table 1 provides the number of departments There were 1,235 new doctoral recipients reported for 2007-08 responding to the 2008 Survey of New Doctoral by departments responding in time for the 2008 First Report. Recipients in time for this report. This year’s The number of departments responding in time for this year's response rates were above 80% for all groups report increased by 18 and in every group except Group I (Pu). except Group IV and increased over last year in There were 540 U.S. citizens reported among this year's new all groups except Group I (Pu). Overall, nineteen doctoral recipients, 44% of the total. Last year's figure was more departments responded in time for the First 43%. Report this year than responded in time for last Based on responses from departments alone, the fall 2008 year’s First Report. Efforts continue to obtain data unemployment rate for the 1,083 new doctoral recipients whose from as many of the non-responding departments employment status is known is 5.4%, up from 4% for fall 2007. as possible. Sixty-nine new doctoral recipients hold positions at the institution that granted their degree, although not necessarily in the same department. This is 7% of the new doctoral recipients who Table 2: New Doctoral Degrees Awarded are currently known to have jobs and 11% of those who have by Group, Preliminary Count academic positions in the U.S. Eighteen new doctoral recipients have part-time positions. Group I (Pu) I (Pr) II III IV Va TOTAL The number of new doctoral recipients employed in the U.S. is 1998–99 292 152 241 136 243 69 1133 886, up 22 from last year. The number of new doctoral recipients 1999–00 256 157 223 132 284 67 1119 employed in academic positions in the U.S. remains relatively stable at 650, it was 651 last year. 2000–01 233 129 203 125 237 81 1008 Of the 886 new doctoral recipients taking positions in the U.S., 2001–02 218 139 164 124 222 81 948 207 (23%) have jobs in business and industry, increasing for 2002–03 258 138 170 121 239 91 1017 the fifth consecutive year. The fall 2008 number is up 11% from 2003–04 195 187 215 111 243 90 1041 fall 2007, and is up 108 (109%) from fall 2004. The number of new doctoral recipients taking jobs in government is up 3 (11%) 2004–05 243 146 203 153 285 86 1116 over fall 2007. 2005–06 307 184 216 140 287 111 1245 Among the 886 new doctoral recipients having employment in the 2006–07 300 119 234 138 279 87 1157 U.S., 426 (48%) are U.S. citizens (up from 405 (47%) last year). The number of non-U.S. citizens having employment in the U.S. 2007–08 234 172 290 142 291 106 1235 is 460; last year it was 459. Among the 307 new doctoral recipients hired by U.S. doctoral- granting departments, 49% are U.S. citizens (up from 48% last year). Among the 342 having other academic positions in the Figure 1: New Doctoral Degrees Awarded U.S., 57% are U.S. citizens (up from 53% last year). by Combined Groups, Preliminary Count Of the 1,235 new doctoral recipients, 31% (388) are female, the same percentage reported in fall 2007. Of the 540 U.S. citizen I (Pu), I (Pr), II, III, & Va new doctoral recipients, 31% (166) are females, up from 29% I (Pu), I (Pr), & II in fall 2007. Among the 540 U.S. citizen new doctoral recipients, 4 are 1000 American Indian or Alaska Native, 23 are Asian, 22 are Black 900 or African American, 19 are Hispanic or Latino, 5 are Native Hawaiian or Other Pacific Islander, 461 are White, and 6 are of 800 unknown race/ethnicity. 700 Group IV produced 291 new doctorates, of which 151 (52%) are 600 females, compared to all other groups combined, where 237 500 (25%) are females. In Group IV, 89 (31%) of the new doctoral recipients are U.S. citizens (while in the other groups 48% are 400 U.S. citizens). 300 Twenty-seven percent of the new doctorates had a dissertation in

Number of Degrees 200 statistics/biostatistics (334). The next highest percentage was 100 in algebra and number theory with 16% (195). 0

The Faculty Salary Survey report, traditionally published as part of 1998-99 1999-00 2007-08 2000–01 2001–02 2002–03 2003–04 2004–05 2005–06 2006–07 this report, will appear in the March issue of Notices.

258 No t i c e s o f t h e AMS Vo l u m e 56, Nu m b e r 2 2008 Annual Survey of the Mathematical Sciences in the U.S.

Figure 2: Percentage of New Doctoral Recipients years. The final count for 2007–08 is likely to be very Unemployed (as reported in the respective close to the final count for 2006–07 of 1,333. Annual Survey Reports 1991–2007) The 2007–08 numbers in Table 2 will be broken down in various ways, such as by sex, in later sections

Preliminary Final of this report. The names of the 1,235 new doctoral recipients are found on pages 276–96 of this issue of 16 the Notices. 14 By way of background to this report on new doctoral 12 recipients, Table 3 gives historical information about various types of full-time graduate students in Groups 10 I, II, III, and Va combined. These data are reprinted 8 from Table 6B of the Third Report of the 2007 Annual 6 Survey (Notices, November 2007). 4

2 Percent Unemployed Employment Plans of 2007–08 New Doctoral 0 Recipients Tables 4A, 4B, and 4C each provide a different cross- tabulation of the 1,235 new doctoral recipients in the 2003-04 1991-92 2005-06 2007-08 1993–94 2001–02 1995–96 1997–98 1999–00 mathematical sciences. These tables contain a wealth of information about these new doctoral recipients, some of which will be discussed in this report. Note Doctoral Degrees Granted in 2007–08 that these tables give a breakdown by sex for type of Table 2 shows the number of new doctoral employer, type of degree-granting department, and field degrees granted by the different doctoral groups of thesis. Keep in mind that the results in this report come surveyed in the Annual Survey for the past from the departments giving the degrees and not from ten years. The preliminary count of 1,235 new the degree recipients themselves. These tables will be doctorates granted by these departments in 2007– updated using information from the doctoral recipients 08 is an increase of 78 from the preliminary count themselves in the 2008 Second Report in the August 2009 issue of Notices. for 2006–07. The last column (Total) in Table 4A can be used to From Table 2 we see that all groups except find the overall unemployment rate. In this and other Group I (Pu) reported an increase in the number unemployment calculations in this report, the individuals of doctoral recipients from the previous year. whose employment status is not known (Unknown The decrease reported for Group I (Pu) is almost (U.S.) and Unknown (non-U.S.)) are first removed, and certainly the result of the four departments the unemployment fraction is the number still seeking in Group I (Pu) that responded in time for last employment divided by the total number of individuals year’s report but not this year’s report. These left after the “Unknowns” are removed. The preliminary departments have awarded an average of 55 unemployment rate for these data is 5.4%. This preliminary doctoral recipients each year over the past four rate will be updated later with information gathered

Table 3: Full-Time Graduate Students in Groups I, II, III, & Va by Sex and Citizenship, Fall 1998 to Fall 2007 (Data Reprinted from Table 6B in Third Report, 2007 Annual Survey)

1998 1999 2000 2001 2002 2003 2004 2005 20062 2007

Total full-time graduate students 8791 8838 9637 9361 9972 10444 10707 10565 10984 10937 Female 2770 2766 3016 2899 3136 3215 3245 3111 3279 3249 % Female 32% 31% 31% 31% 31% 31% 30% 29% 30% 30% % U.S. citizen 55% 53% 53% 49% 51% 54% 55% 56% 56% 56% % Underrepresented minorities1 10% 9% 10% 9% 9%

Total first-year graduate students 2458 2664 2839 2875 2996 2711 3004 2832 2960 2964 Female 859 866 879 1014 1038 902 983 851 961 950 % Female 35% 33% 31% 35% 35% 33% 33% 30% 32% 32% % U.S. citizen 55% 53% 54% 53% 55% 56% 60% 59% 55% 56% % Underrepresented minorities 12% 9% 10% 10% 10%

1 Underrepresented minorities includes any person having origins within the categories American Indian or Alaska Native, Black or African American, Hispanic or Latino, and Native Hawaiian or Other Pacific Islander. 2 Numbers in this column reflect corrections of those previously reported. For further information visit our website at http://www.ams.org/employment/surveyreports.html.

Fe b r u a r y 2009 No t i c e s o f t h e AMS 259 2008 Annual Survey of the Mathematical Sciences in the U.S.

Table 4A: Employment Status of 2007–08 New Doctoral Recipients in the Mathematical Sciences by Field of Thesis FIELD OF THESIS

Real, Comp., Discr. Math./ Numerical Linear Differential, Algebra/ Funct., & Combin./ Analysis/ Nonlinear Integral, & Number Harmonic Geometry/ Logic/ Statistics/ Applied Approxi- Optim./ Difference Math. Other/ TYPE OF EMPLOYER Theory Analysis Topology Comp. Sci. Probability Biostat. Math. mations Control Equations Educ. Unknown TOTAL Group I (Public) 27 6 13 3 5 1 6 5 3 8 0 0 77 Group I (Private) 17 1 17 5 3 2 8 1 0 6 0 0 60 Group II 14 11 8 5 1 4 9 6 2 12 2 1 75 Group III 14 2 2 2 1 8 4 2 2 2 5 0 44 Group IV 0 0 0 0 1 41 0 0 0 0 0 0 42 Group Va 0 0 1 1 0 0 7 0 0 0 0 0 9 Master’s 8 4 3 6 1 11 6 7 1 4 3 0 54 Bachelor’s 27 9 16 15 2 12 22 3 2 14 4 0 126 Two-Year College 2 4 2 2 0 1 5 1 0 4 1 0 22 Other Academic Dept. 7 2 2 8 1 54 27 4 3 3 0 0 111 Research Institute/ 2 0 1 3 1 12 7 1 0 2 0 0 29 Other Nonprofit Government 0 0 2 2 0 17 6 1 1 1 0 0 30 Business and Industry 14 8 10 10 18 104 23 8 2 8 0 2 207 Non-U.S. Academic 20 7 16 10 5 15 23 0 3 10 0 0 109 Non-U.S. Nonacademic 4 0 0 1 2 7 0 4 0 2 0 0 20

Not Seeking Employment 3 0 1 0 0 3 1 0 0 2 0 0 10 Still Seeking Employment 13 5 6 4 3 7 9 3 0 8 0 0 58 Unknown (U.S.) 15 5 6 6 2 23 17 8 3 8 1 1 95 Unknown (non-U.S.)* 8 2 8 6 2 12 9 4 0 5 0 1 57 TOTAL 195 66 114 89 48 334 189 58 22 99 16 5 1235 Column Male 156 50 92 63 43 164 131 48 18 69 8 5 847 Subtotals Female 39 16 22 26 5 170 58 10 4 30 8 0 388

*Includes those whose status is reported as “unknown” or “still seeking employment”.

Table 4B: Employment Status of 2007–08 New Doctoral Recipients in the Mathematical Sciences by Type of Degree-Granting Department

TYPE OF DOCTORAL DEGREE-GRANTING DEPARTMENT Group I Group I Row (Public) (Private) Group II Group III Group IV Group Va Subtotals TYPE OF EMPLOYER Math. Math. Math. Math. Statistics Applied Math. TOTAL Male Female Group I (Public) 30 20 15 6 1 5 77 62 15 Group I (Private) 12 37 4 1 3 3 60 48 12 Group II 23 9 27 10 3 3 75 56 19 Group III 9 1 15 13 5 1 44 31 13 Group IV 0 0 1 1 39 1 42 21 21 Group Va 0 2 2 0 0 5 9 9 0 Master’s 12 3 20 6 12 1 54 39 15 Bachelor’s 25 7 59 21 8 6 126 76 50 Two-Year College 6 1 7 5 1 2 22 18 4 Other Academic Dept. 7 6 18 13 49 18 111 60 51 Research Institute/ 2 4 6 1 12 4 29 13 16 Other Nonprofit Government 3 4 4 1 16 2 30 18 12 Business and Industry 24 19 32 22 87 23 207 132 75 Non-U.S. Academic 34 27 16 8 16 8 109 88 21 Non-U.S. Nonacademic 4 4 4 1 4 3 20 18 2 Not Seeking Employment 2 0 2 3 2 1 10 2 8 Still Seeking Employment 21 8 12 11 3 3 58 44 14 Unknown (U.S.) 7 12 28 13 22 13 95 73 22 Unknown (non-U.S.)* 13 8 18 6 8 4 57 39 18 TOTAL 234 172 290 142 291 106 1235 847 388 Column Male 184 143 207 96 140 77 847 Subtotals Female 50 29 83 46 151 29 388 *Includes those whose status is reported as “unknown” or “still seeking employment”.

260 No t i c e s o f t h e AMS Vo l u m e 56, Nu m b e r 2 2008 Annual Survey of the Mathematical Sciences in the U.S.

Table 4C: Field of Thesis of 2007–08 New Doctoral Recipients by Type of Degree-Granting Department

FIELD OF THESIS TYPE OF DOCTORAL Real, Comp., Discr. Math./ Numerical Linear Differential, DEGREE-GRANTING Algebra/ Funct., & Combin./ Analysis/ Nonlinear Integral, & Number Harmonic Geometry/ Logic/ Statistics/ Applied Approxi- Optim./ Difference Math. Other/ DEPARTMENT Theory Analysis Topology Comp. Sci. Probability Biostat. Math. mations Control Equations Educ. Unknown TOTAL Group I (Public) 61 16 35 33 12 2 34 6 6 26 0 3 234 Group I (Private) 56 12 34 12 10 0 27 2 2 17 0 0 172 Group II 64 24 32 16 12 15 61 27 5 27 7 0 290 Group III 14 12 9 14 4 20 19 16 4 19 9 2 142 Group IV 0 0 0 0 4 277 9 0 0 1 0 0 291 Group Va 0 2 4 14 6 20 39 7 5 9 0 0 106 Column Total 195 66 114 89 48 334 189 58 22 99 16 5 1235

Table 5A: 2007–08 New Doctoral Recipients Employed in the Table 5B: Number of New Doctoral U.S by Type of Degree-Granting Department Recipients Taking Positions in Business and Industry in the U.S. by Type of Degree- Group Granting Department, Fall 2004 to Fall 2008 Type of Employer in U.S. I (Pu) I (Pr) II III IV Va TOTAL Group Groups I, II, III, IV, and Va 74 69 64 31 51 18 307 Year I (Pu) I (Pr) II III IV Va TOTAL Master’s, Bachelor’s, and 2-Year Colleges 43 11 86 32 21 9 202 Fall 2004 9 13 9 9 50 9 99 Other Academic and Fall 2005 5 9 14 15 64 8 115 Research Institutes 9 10 24 14 61 22 140 Fall 2006 27 14 19 9 80 18 167 Government 3 4 4 1 16 2 30 Fall 2007 39 10 16 19 88 15 187 Business and Industry 24 19 32 22 87 23 207 Fall 2008 24 19 32 22 87 23 207 TOTAL 153 113 210 100 236 74 886

from the individual new doctoral recipients. The new doctoral recipients entering the business and additional information from prior years is reflected industry sector more than doubled, from 99 to in the final unemployment rates displayed in 207, an increase of 108. In addition, the fall 2008 Figure 2. The preliminary rate for fall 2007 was number is up 11% from fall 2007. 4.0%. The unemployment rates, calculated by type Among the 886 new doctoral recipients known of doctoral degree-granting department using Table to have employment in the U.S. in fall 2008, 4B, vary from group to group, with a high of 9.8% for Group I (Pu) has the smallest percentage taking Group I (Pu) and a low of 1.1% for Group IV. jobs in business and industry at 16% and Group IV There are 886 new doctoral recipients employed the highest at 37%. in the U.S. Table 5A gives a breakdown of type of Table 5C shows the number of new doctoral employer by type of degree-granting department recipients who took academic positions in the U.S. for these 886 new doctoral recipients. Of these, 649 by type of department granting their degree for fall (73%) hold academic positions, 30 (3%) are employed 2004 to fall 2008. The total number of new doctoral by government, and 207 (23%) hold positions in recipients taking academic employment in fall 2008 business and industry. In the First Report for is relatively unchanged from fall 2007. Among the 886 new doctoral recipients employed in the U.S. 2006–07, there were 864 new doctoral recipients in fall 2008, 73% have academic positions. This employed in the U.S., of which 650 (75%) held academic positions, 27 (3%) were in government, Table 5C: Number of New Doctoral and 187 (22%) were in business and industry. The Recipients Taking U.S. Academic Positions by number of new doctoral recipients employed in the Type of Degree-Granting U.S. increased in all categories except Group I–Va Department, Fall 2004 to Fall 2008 which decreased 4%. “Business and Industry” and Group "Government" showed the largest increase at 11%. Table 5B shows the number of new doctoral Year I (Pu) I (Pr) II III IV Va TOTAL recipients who took positions in business and Fall 2004 110 113 130 70 142 49 614 industry by the type of department granting their Fall 2005 131 88 130 83 131 39 602 degree for fall 2004 to fall 2008. The number of Fall 2006 167 108 123 86 137 50 671 new doctoral recipients taking jobs in business and industry has been steadily increasing since Fall 2007 178 76 146 87 120 43 650 2004. From fall 2004 to fall 2008, the number of Fall 2008 126 90 174 77 133 49 649

Fe b r u a r y 2009 No t i c e s o f t h e AMS 261 2008 Annual Survey of the Mathematical Sciences in the U.S.

Table 5D: Academic Positions in U.S. Filled Table 5E: Females as a Percentage of 2007–08 by New Doctoral Recipients by Type of New Doctoral Recipients Produced by and Hiring Department, Fall 2004 to Fall 2008 Hired by Doctoral-Granting Groups

Group Group Percent I (Pu) I (Pr) II III IV Va TOTAL Year I–III IV Va M&B Other* TOTAL Produced 21% 17% 29% 32% 52% 27% 31% Fall 2004 222 63 17 154 158 614 Hired 19% 20% 25% 30% 50% 0% 26% Fall 2005 231 45 12 188 126 602 Fall 2006 262 69 12 185 143 671 unchanged from 30 in fall 2007 to 29 in fall Fall 2007 264 39 17 186 144 650 2008. Fall 2008 256 42 9 180 162 649 In fall 2008, 69 new doctoral recipients held *Includes other academic and research institutes/nonprofit. positions in the institution that granted their degree, although not necessarily in the same percentage is highest for Group II at 83% and lowest department. This represents 7% of new doctoral for Groups IV at 56%. recipients who are currently employed in the U.S. Table 5D shows the number of positions filled and 11% of the U.S. academic positions held by with new doctoral recipients for each type of new doctoral recipients. In fall 2007 there were 78 academic employer. Increases in positions filled such individuals making up 8% of the new doctoral by new doctoral recipients were realized only by recipients who were employed at the time of the First Report. Eighteen new doctoral recipients have Groups IV and Other. The biggest increase in hires taken part-time positions in fall 2008 compared of new doctorates into academic positions was in with 22 in fall 2007. Group Other (13%). Hires of new doctorates into positions at research institutes remained relatively Information about 2007–08 Female New Doctoral Recipients Table 5G: 2007–08 New Doctoral Tables 4A and 4B give male and female Recipients Having Employment in the U.S. breakdowns of the new doctoral recipients in 2007– by Type of Employer and Citizenship 08 by Field of Thesis, by Type of Degree-Granting CITIZENSHIP Department, and by Type of Employer. U.S. EMPLOYER U.S. Non-U.S. TOTAL Overall, 388 (31%) of the 1,235 new doctoral Academic 344 305 649 recipients in 2007–08 are female. In 2006–07, 365 Groups I–Va 149 158 307 (32%) of the new doctoral recipients were female. M, B, & 2-Year 129 73 202 This percentage varies over the different groups, Other Acad. & Research Inst. 66 74 140 and these percentages are given in the first row Government, Business & Industry 82 155 237 of Table 5E. This year the percentage of females TOTAL 426 460 886 produced is highest again for Group IV at 52%,

Table 5F: Employment Status of 2007–08 New Doctoral Recipients by Citizenship Status

CITIZENSHIP

NON-U.S. CITIZENS U.S. CITIZENS TOTAL TYPE OF EMPLOYER Permanent Visa Temporary Visa Unknown Visa U.S. Employer 426 52 395 13 886

U.S. Academic 344 32 265 8 649 Groups I, II, III, and Va 132 9 120 4 265 Group IV 17 1 23 1 42 Non-Ph.D. Department 182 22 107 2 313 Research Institute/Other Nonprofit 13 0 15 1 29 U.S. Nonacademic 82 20 130 5 237 Non-U.S. Employer 29 2 95 3 129 Non-U.S. Academic 27 1 78 3 109 Non-U.S. Nonacademic 2 1 17 0 20 Not Seeking Employment 6 1 3 0 10 Still Seeking Employment 26 3 29 0 58 SUBTOTAL 487 58 522 16 1083 Unknown (U.S.) 53 4 34 4 95 Unknown (non-U.S.)* 0 1 53 3 57

TOTAL 540 63 609 23 1235

*Includes those whose status is reported as “unknown” or “still seeking employment”.

262 No t i c e s o f t h e AMS Vo l u m e 56, Nu m b e r 2 2008 Annual Survey of the Mathematical Sciences in the U.S.

Table 6: Sex, Race/Ethnicity, and Citizenship of 2007–08 New Doctoral Recipients

MALE FEMALE NON-U.S. CITIZENS NON-U.S. CITIZENS U.S. Permanent Temporary Unknown Total U.S. Permanent Temporary Unknown Total RACIAL/ETHNIC GROUP CITIZENS Visa Visa Visa Male CITIZENS Visa Visa Visa Female TOTAL American Indian or 2 0 0 0 2 2 0 1 0 3 5 Alaska Native Asian 11 11 263 4 289 12 9 135 10 166 455 Black or African 11 8 17 0 36 11 1 1 0 13 49 American Hispanic or Latino 19 2 22 0 43 0 1 5 1 7 50 Native Hawaiian or 5 0 1 0 6 0 0 0 0 0 6 Other Pacific Islander White 324 17 120 2 463 137 13 39 2 191 654 Unknown 2 1 3 2 8 4 0 2 2 8 16 TOTAL 374 39 426 8 847 166 24 183 15 388 1235 compared with 46% last year. The second row of the similar percentage for non-U.S. citizens with Table 5E gives the percentage of the new doctoral a temporary visa is 76% (last year the percentage recipients hired who are female for each of the was 77%). The number of non-U.S. citizens having Groups I, II, III, IV, and Va. In addition, 28% of the employment in the U.S. is 460, relatively unchanged new doctoral recipients hired in Group M, master’s from last year (459). departments, are female; 40% of the new doctoral Table 5G is a cross-tabulation of the 886 new recipients hired in Group B, bachelor’s departments, doctoral recipients who have employment in are female, up from 37% last year. This year, the U.S. by citizenship and broad employment Group IV hired the highest percentage of women categories, using numbers from Table 5F. Of the with 50%, while Groups I, II, III ranged from 19 to 886 new doctoral recipients having jobs in the U.S., 30%, and Group Va hired no women. 48% are U.S. citizens (up from 47% last year). Of the The unemployment rate for female new doctoral 307 new doctoral recipients who took jobs in U.S. recipients is 4%, compared to 6% for males and 5.4% doctoral-granting departments, 49% are U.S. citizens overall. (up from 48% last year). Of the 342 who took other The percentage of female new doctoral recipients academic positions, 57% are U.S. citizens (up from within fields of thesis ranged from 10% in probability, 53% last year). Of the 237 who took nonacademic to 50% in mathematics education and 51% in positions, 35% are U.S. citizens. Of the 426 U.S. statistics. citizens employed in the U.S., 35% have jobs in a Later sections in this First Report give more doctoral-granting department, 46% are in other information about the female new doctoral academic positions, and 19% are in nonacademic recipients by citizenship and the female new positions. For the 460 non-U.S. citizens employed doctoral recipients in Group IV. in the U.S., the analogous percentages are 34%, 32%, and 34% respectively.

Employment Information about 2007–08 New Doctoral Recipients by Citizenship Sex, Race/Ethnicity, and Citizenship Status of and Type of Employer 2007–08 New Doctoral Recipients Table 5F shows the pattern of employment within Table 6 presents a breakdown of new doctoral employer categories broken down by citizenship recipients according to sex, racial/ethnic group, status of the new doctoral recipients. and citizenship status. The information reported The unemployment rate for the 540 U.S. in this table was obtained in summary form from citizens is 5.3% compared to 5.1% in fall 2007. The the departments granting the degrees. unemployment rate for non-U.S. citizens is 5.4%. There were 540 (44%) U.S. citizens among the This varies by type of visa. The unemployment rate 1,235 new doctoral recipients in 2007–08. Among for non-U.S. citizens with a permanent visa is 5.2%, U.S. citizens, 4 are American Indian or Alaska Native while that for non-U.S. citizens with a temporary (2 male and 2 female), 23 are Asian (11 males and visa is 5.6%. Among U.S. citizens whose employment 12 females), 22 are Black or African American (11 status is known, 87% are employed in the U.S. males and 11 female), 19 are Hispanic or Latino Among non-U.S. citizens with a permanent visa (males), 5 are Native Hawaiian or Other Pacific whose employment status is known, 90% have jobs Islander (males), 461 are White (324 males and 137 in the U.S. (last year this percentage was 95%), while females), and 6 are of unknown race/ethnicity (2

Fe b r u a r y 2009 No t i c e s o f t h e AMS 263 2008 Annual Survey of the Mathematical Sciences in the U.S.

Table 7: U.S. Citizen Doctoral Recipients, Figure 3: U.S. Citizen Doctoral Recipients, Preliminary Counts Preliminary Counts

Total Doctorates Total U.S. Total Doctorates Granted by U.S. Institutes Granted by U.S. Citizen Doctoral Year Institutions Total % Total U.S. Citizen Doctoral Recipients 1997–98 1216 586 48% 1300 1998–99* 1133 554 49% 1200 1999–00 1119 537 48% 1100 2000–01 1008 494 49% 1000 2002–03 1017 489 48% 900 2003–04 1041 441 42% 800 2004–05 1116 433 39% 700 2005–06 1245 522 42% 600 2006–07 1157 500 43% 500 2007–08 1235 540 44% 400 *Prior to 1998–99, the counts include new doctoral recipients from Group Vb. In addition, prior to 1982–83, the counts include recipients 300 from computer science departments. 200 100 Table 8: Sex of U.S. Citizen 0 Doctoral Recipients, Preliminary Counts

Total U.S. 2002-03 2000-01 2004-05 2006-07 1990–91 1996–97 1992–93 Citizen Doctoral % 1988–89 1994–95 1998–99 Year Recipients Male Female Female Figure 4: Females as a Percentage of U.S. Citizen Doctoral 1997–98 586 423 163 28% Recipients and Graduate Students, Preliminary Counts 1998–99* 554 367 187 34% % Female U.S. Doctoral Recipients 1999–00 537 379 158 29% 2000–01 494 343 151 31% % Female U.S. Graduate Students 2002–03 489 332 157 32% 40% 2003–04 441 297 144 33% 2004–05 433 313 120 28% 35% 2005–06 522 379 143 27% 30% 2006–07 500 355 145 29% 2007–08 540 374 166 31% 25% *Prior to 1998–99, the counts include new doctoral recipients from Group Vb. In addition, prior to 1982–83, the counts include recipients 20% from computer science departments.

15% males and 4 females). Among non-U.S. citizens, there are 1 American Indian 10% or Alaska Native, 432 Asians, 27 Blacks or African Americans, 31 Hispanics or 5% Latinos, 1 Native Hawaiian or Other Pacific Islander, 193 Whites, and 10 are 0% of unknown race/ethnicity. Table 7 (and Figure 3) gives the number of new U.S. doctoral recipients and the 2000-01 2002-03 2004-05 2006-07 1988–89 1990–91 1992–93 1994–95 1996–97 1998–99 number of U.S. citizens back to 1997-98. The 540 U.S. citizen new doctoral recipients is up Table 8 (and Figure 4) gives the historical record by 46 (8%) from 2000–01. The percentage of U.S. of U.S. citizen new doctoral recipients, broken down citizen new doctoral recipients has increased this by male and female for past years, going back to year to 44% from 43% in fall 2007. 1997–98. The number of female U.S. citizen new Females make up 31% of the 540 U.S. citizens doctoral recipients is up 15 (10%) from 151 in receiving doctoral degrees in the mathematical sciences in 2007–08. Last year this percentage was 2000–01 and down 11% from an all-time high of 187 29%. Among the 695 non-U.S. citizen new doctoral in 1998–99. Figure 4 also displays the percentage recipients, 32% (222) are female, down from last of females among U.S. citizen (full-time) graduate year’s 33%. students beginning in fall 1988.

264 No t i c e s o f t h e AMS Vo l u m e 56, Nu m b e r 2 2008 Annual Survey of the Mathematical Sciences in the U.S.

Table 9: Sex and Citizenship of 2007–08 New Doctoral Recipients by Type of Degree–Granting Department

GROUP I (Pu) I (Pr) II III IV Va TOTAL CITIZENSHIP Male Female Male Female Male Female Male Female Male Female Male Female Male Female U.S. 79 26 72 8 105 43 39 25 39 50 40 14 374 166 Non-U.S. 105 24 71 21 102 40 57 21 101 101 37 15 473 222 TOTAL 184 50 143 29 207 83 96 46 140 151 77 29 847 388

Table 9 gives a sex and citizenship breakdown between the 57 statistics departments and the of the new doctorates within each of the six groups 32 biostatistics and biometrics departments in of doctoral-granting departments. Among all 1,235 Group IV. This year 382 new doctorates had a new doctoral recipients, 44% of the males and 43% dissertation in statistics/biostatistics (334) or of the females are U.S. citizens. probability (48), a slight increase from last year’s number. Those with dissertations in statistics/ biostatistics and probability accounted for 31% 2007–08 New Doctoral Recipients with of new doctorates in 2007–08. Quite a bit of the Dissertations in Statistics/Biostatistics variation in numbers from year to year in Table 10 and Probability is due to the changes made in the departments in Group IV contains U.S. departments (or programs) Group IV over the ten years and to the relatively of statistics, biostatistics, and biometrics reporting low response rate for this group. At the time of the a doctoral program. In the Annual Survey Reports, Second Report last year, 70 of 88 (80%) of Group IV Group IV is referred to as the Statistics Group. departments had responded. In addition, other groups in the Annual Survey Group IV has 89 departments for 2007–08, produce new doctoral recipients with dissertations 14 more than the next largest doctoral group. It in statistics/biostatistics or probability. The other contains 31% of all doctoral departments surveyed, groups produced 101 new doctoral recipients with and the 60 Group IV departments responding dissertations in statistics/biostatistics or probability to the Annual Survey reported 291 new doctoral in 2007–08 and have averaged 84.4 per year over the recipients, 24% of all new doctoral recipients in ten-year period reported in Table 10. Information 2007–08. The number of new doctoral recipients about these 101 new doctoral recipients and the 281 in Group IV is up 12 from the number reported at new doctoral recipients in Group IV is found in this this time last year, while the number of departments section of the report. responding is up 10 from the number responding Table 10 contains information about new by this time last year. doctoral recipients in Group IV as well as those Because of its size, the data from Group IV have a with dissertations in statistics/biostatistics and large effect on the results when all doctoral groups probability in other groups for this year as well as are combined. Furthermore, Group IV results for the past nine years. In addition, the last two are often quite different from those for Groups rows of Table 10 give a split of the 2007–08 results I (Pu), I (Pr), II, III, and Va. Group IV results can

Table 10: New Doctoral Recipients with Dissertations in Statistics/Biostatistics and Probability

New Doctoral Recipients in Statistics/Biostatistics New Doctoral Recipients Group IV New Doctoral Recipients in Group IV only and Probability, Group IV and Other* Groups Hired by Group IV Group IV Depts Depts Responding Female Jobs in Percentage Other Percentage Year Surveyed (percent) Total (percent) Bus & Ind Unemployed Total Group IV Groups Unemployed Male Female 1998–99 91 72 (79%) 243 87 (36%) 57 4.9% 320 240 80 5.8% 29 20 1999–00 89 75 (84%) 284 110 (39%) 79 2.4% 351 278 73 2.0% 24 22 2000–01 86 70 (81%) 237 98 (41%) 59 5.1% 289 221 68 5.3% 27 14 2001–02 86 72 (84%) 222 92 (41%) 56 6.0% 288 221 67 5.4% 31 15 2002–03 86 74 (86%) 239 98 (41%) 45 2.1% 302 234 68 3.3% 20 19 2003–04 87 65 (75%) 243 97 (40%) 50 3.0% 318 241 77 4.0% 48 15 2004–05 87 63 (72%) 285 126 (44%) 64 4.5% 374 283 91 5.4% 26 19 2005–06 88 60 (68%) 287 134 (47%) 80 1.6% 396 278 118 2.0% 41 28 2006–07 86 50 (58%) 279 127 (46%) 88 2.9% 380 279 101 3.9% 24 15 2007–08 89 59 (66%) 291 151 (52%) 87 1.1% 382 281** 101*** 2.9% 21 21 Statistics 57 43 (75%) 215 100 (47%) 68 1.1% 10 11 Biostatistics 32 16 (50%) 76 51 (67%) 18 1.0% 11 10

* Includes other academic departments and research institutes/other nonprofits. ** Of 281, there were 277 in statistics/biostatistics and 4 in probability. For complete details, see Table 4C. *** Of 101, there were 57 in statistics/biostatistics and 44 in probability. For complete details, see Table 4C.

Fe b r u a r y 2009 No t i c e s o f t h e AMS 265 2008 Annual Survey of the Mathematical Sciences in the U.S.

mask important changes in the other doctoral groups. available on the AMS website at www.ams.org/ In the following paragraphs some of these differences employment/surveyreports.html. are presented. The trends noted below have also been observed in past reports. Acknowledgments Group IV is producing a larger percentage of female The Annual Survey attempts to provide an accurate doctorates than the other doctoral groups. Table 9 shows appraisal and analysis of various aspects of the that for the Group IV new doctoral recipients, 151 of 291 academic mathematical sciences scene for the use (52%) are female, while 237 of 944 (25%) are female in and benefit of the community and for filling the the other doctoral groups. Among U.S. citizens, females information needs of the professional organizations. accounted for 50 of the 89 (56%) Group IV new doctoral Every year, college and university departments recipients, while for the other groups 116 of 451 (26%) in the United States are invited to respond. The were female. Overall, 166 of 540 (31%) U.S. citizen new Annual Survey relies heavily on the conscientious doctoral recipients were female. efforts of the dedicated staff members of these Group IV is producing a smaller percentage of U.S. departments for the quality of its information. citizen new doctorates than the other doctoral groups. On behalf of the Annual Survey Data Committee In Group IV, 89 of 291 (31%) new doctoral recipients are and the Annual Survey Staff, we thank the many U.S. citizens, while in other groups 451 of 944 (48%) are secretarial and administrative staff members in U.S. citizens. In Group IV, 101 (69%) of the 151 females the mathematical sciences departments for their were not U.S. citizens. cooperation and assistance in responding to the Group IV doctorates are more likely to take jobs survey questionnaires. in business and industry than those in other doctoral groups. Of the 236 new doctoral recipients from Other Data Sources Group IV who found employment in the U.S., 87 (37%) American Association of University Professors, The took jobs in business or industry. From the other Annual Report on the Economic Status of the Profession groups, 650 new doctoral recipients found employment 2007–2008, Academe: Bull. AAUP (March/April 2008), in the U.S., of which 120 (18%) took jobs in business or Washington, DC. industry. Commission on Professionals in Science and Technology, Group IV doctorates have a lower unemployment Professional Women and Minorities, 17th ed., CPST, rate than the other doctoral groups. The employment Washington, DC, 2008. status for 261 Group IV new doctoral recipients is known, Conference Board of the Mathematical Sciences, Statistical and 3 (1.1%) are unemployed. For the other groups, the Abstract of Undergraduate Programs in the Mathemati- employment status of 822 is known, and 55 (6.7%) are cal Sciences in the United States: Fall 2005 CBMS Survey, unemployed. Group IV is hiring a bigger percentage of American Mathematical Society, Providence, RI, 2007. females than the other doctoral groups. Twenty-one ——— , Statistical Abstract of Undergraduate Programs of 42 (50%) new doctoral recipients hired by Group IV in the Mathematical Sciences in the United States: Fall departments were female, up from last year’s 38% and 2000 CBMS Survey, American Mathematical Society, the first-time female hires has equaled male hires. The Providence, RI, 2002. other doctoral groups reported that 59 of 265 (22%) new National Opinion Research Center, Doctorate Recipients doctoral recipients hired were female, down from last from United States Universities: Summary Report 2006, year’s 30%. Survey of Earned Doctorates, Chicago, IL, 2006. Group IV had 281 new doctoral recipients with fields National Research Council, Strengthening the Linkages of thesis in statistics/biostatistics (277) and the other between the Sciences and the Mathematical Sciences, doctoral departments had 101 with fields of thesis in National Academy Press, Washington, DC, 2000. statistics/biostatistics (57) and probability (44) (last year ——— , U.S. Research Institutes in the Mathematical Sciences: the other doctoral departments had 60 new doctorates Assessment and Perspectives, National Academy Press, in statistics and 41 in probability). The distribution of Washington, DC, 1999. these degrees among the various groups can be found National Science Board, Science and Engineering Indica- in Table 4C. The number of new doctoral recipients with tors—2008. Two volumes. (volume 1, NSB 08–01; theses in statistics/biostatistics and probability (382) is volume 2, NSB 08–01A), National Science Foundation, substantially larger than any other field, with algebra and Arlington, VA, 2006. number theory next with 195. National Science Foundation, U.S. Doctorates in the 20th Century (NSF 06-319), Arlington, VA, 2006 ——— , Characteristics of Doctoral Scientists and Engineers Previous Annual Survey Reports in the United States: 2003 (NSF 06-329), Detailed Statis- The 2007 First, Second, and Third Annual Survey Re- tical Tables, Arlington, VA, 2006. ports were published in the Notices of the AMS in the ——— , Graduate Students and Postdoctorates in Science February, August, and November 2008 issues respec- and Engineering: Fall 2008 (NSF 08-306), Arlington, tively. These reports and earlier reports, as well as a VA, 2006. (http://www.nsf.gov/statistics/ wealth of other information from these surveys, are nsf08306)

266 No t i c e s o f t h e AMS Vo l u m e 56, Nu m b e r 2 2008 Annual Survey of the Mathematical Sciences in the U.S.

——— , Plans for Postdoctoral Research Appointments Among Recent U.S. Doctorate Recipients (NSF 04-308), Definitions of the Groups Arlington, VA, 2004. As has been the case for a number of years, much of the data in these , Science and Engineering Degrees: 1966–2006. ——— reports is presented for departments divided into groups according Detailed Statistical Tables (NSF 08-321), Arlington, to several characteristics, the principal one being the highest degree VA, 2006. (http://www.nsf.gov/statistics/ offered in the mathematical sciences. Doctoral-granting departments nsf08321) of mathematics are further subdivided according to their ranking ——— , Science and Engineering Degrees, by Race/Eth- of “scholarly quality of program faculty” as reported in the 1995 nicity of Recipient: 1995–2004. January 2007. NSF publication Research-Doctorate Programs in the United States: 07-308), Arlington, VA. Continuity and Change.1 These rankings update those reported in a 2 ——— , Science and Engineering Doctorate Awards: 2005 previous study published in 1982. Consequently, the departments (NSF 07-305), Arlington, VA, 2004. which now compose Groups I, II, and III differ significantly from those used prior to the 1996 survey. ———, Women, Minorities, and Persons with Disabilities in Science and Engineering: 2007 (NSF 07-315), The subdivision of the Group I institutions into Group I Public Arlington, VA, 2004. (http://www.nsf.gov/ and Group I Private was new for the 1996 survey. With the increase statistics/wmpd) in number of the Group I departments from 39 to 48, the Annual Survey Data Committee judged that a further subdivision of public and private would provide more meaningful reporting of the data for these departments. Brief descriptions of the groupings are as follows: Group I is composed of 48 departments with scores in the 3.00–5.00 range. Group I Public and Group I Private are Group I departments at public institutions and private institutions respectively. Group II is composed of 56 departments with scores in the 2.00–2.99 range. Group III contains the remaining U.S. departments reporting a doctoral program, including a number of departments not included in the 1995 ranking of program faculty. Group IV contains U.S. departments (or programs) of statistics, biostatistics, and biometrics reporting a doctoral program. Group V contains U.S. departments (or programs) in applied mathematics/applied science, operations research, and management science which report a doctoral program. Group Va is applied mathematics/applied science; Group Vb, which was no longer surveyed as of 1998–99, was operations research and management science. Group M contains U.S. departments granting a master’s degree as the highest graduate degree. Group B contains U.S. departments granting a baccalaureate degree only. Listings of the actual departments which compose these groups are available on the AMS website at www.ams.org/employment/ groups_des.html.

1Research-Doctorate Programs in the United States: Continuity and Change, edited by Marvin L. Goldberger, Brendan A. Maher, and Pamela Ebert Flattau, National Academy Press, Washington, DC, 1995. 2These findings were published in An Assessment of Research- Doctorate Programs in the United States: Mathematical and Physical Sciences, edited by Lyle V. Jones, Gardner Lindzey, and Porter E. Coggeshall, National Academy Press, Washington, DC, 1982. The information on mathematics, statistics, and computer science was presented in digest form in the April 1983 issue of the Notices of the AMS, pages 257–67, and an analysis of the classifications was given in the June 1983 Notices of the AMS, pages 392–3.

Fe b r u a r y 2009 No t i c e s o f t h e AMS 267 Mathematics People

Srinivas Receives TWAS Prize Strassen Awarded ACM Knuth in Mathematics Prize Vasudevan Srinivas of the Tata Institute of Fundamental Volker Strassen of the University of Konstanz has been Research, Mumbai, has been named the winner of the 2008 awarded the 2008 Knuth Prize of the Association for TWAS Prize in Mathematics, awarded by the Academy of Computing Machinery (ACM) Special Interest Group on Sciences for the Developing World (TWAS). He was hon- Algorithms and Computation Theory (SIGACT). He was ored “for his basic contributions to algebraic geometry honored for his contributions to the theory and practice that have helped deepen our understanding of cycles, of algorithm design. The award carries a cash prize of motives, and K-theory.” Srinivas will receive a cash prize US$5,000. of US$15,000 and will deliver a lecture at the academy’s According to the prize citation, “Strassen’s innovations twentieth general meeting, to be held in South Africa in enabled fast and efficient computer algorithms, the se- September 2009. quence of instructions that tells a computer how to solve a

particular problem. His discoveries resulted in some of the —From a TWAS announcement most important algorithms used today on millions if not billions of computers around the world and fundamentally altered the field of cryptography, which uses secret codes Pujals Awarded ICTP/IMU to protect data from theft or alteration.” Ramanujan Prize His algorithms include fast matrix multiplication, integer multiplication, and a test for the primality of integers. Enrique R. Pujals, associate researcher at the Instituto His discovery of provably fast algorithms to determine Nacional de Matemática Pura e Aplicada (IMPA), Brazil, whether a number is prime or composite “profoundly has been awarded the 2008 Srinivasa Ramanujan Prize in changed the cryptography field.” Strassen has also proved recognition of “his outstanding contributions to dynamical fundamental theorems in statistics, including “Strassen’s systems, especially the characterization of robust dynam- law of the iterated logarithm” and the principle of strong ics for flows and transformations and the development of invariance. He is considered the founding father of alge- a theory of generic systems.” braic complexity theory with his work on the degree bound The prize is awarded annually by the Abdus Salam connecting complexity to algebraic geometry. He also International Centre for Theoretical Physics (ICTP), and introduced fundamental notions and results in bilinear the prizewinner is selected by ICTP through a committee complexity and tensor rank. of five eminent mathematicians appointed in conjunction with the International Mathematical Union (IMU). The prize The Knuth Prize is given at one-and-a-half-year inter- recognizes a researcher from a developing country who vals by ACM SIGACT and the Institute of Electrical and is less than forty-five years of age on December 31 of the Electronics Engineers (IEEE) Technical Committee on the year of the award and who has conducted outstanding re- Mathematical Foundations of Computer Science. It is search in a developing country. Funding for the US$10,000 presented in honor of Donald Knuth, professor emeritus cash award is provided by the Niels Henrik Abel Memo- at Stanford University, who has played a critical role in rial Fund through the participation of the International establishing and defining computer science as a rigorous Mathematical Union. intellectual discipline.

—From an ICTP announcement —From an ACM announcement

268 Notices of the AMS Volume 56, Number 2 Mathematics People

and alternatives. In AHP-based decisions, final weights Ozawa Receives Operator allow alternatives to be compared and ranked. Algebra Prize The INFORMS Impact Prize, awarded once every two years, recognizes contributions that have had a broad Narutaka Ozawa of the University of Tokyo has been practical impact on operations research and related fields, awarded the third Operator Algebra Prize for his out- such as the decision sciences. standing contributions to the structure theory of type II1 von Neumann algebras related to the theory of discrete —From an INFORMS announcement groups and thus to the advancement of operator algebra theory. The prize consists of a cash award of about US$3,000, a prize certificate, and a medal. Vybiral Receives 2008 Ozawa has given a series of stunning results on the structure of operator algebras in connection with discrete Information-Based Complexity groups. He first gave a characterization of exactness of discrete groups, which showed groups claimed by Gromov Young Researcher Award are not exact, thus solving a long-standing open problem. Jan Vybiral of the University of Jena, Germany, has been He has further introduced the notion of a solid von Neu- awarded the Information-Based Complexity Award for mann algebra, which means that the relative commutant 2008. The award is given every year for significant con- of any diffuse subalgebra is injective, and has shown that tributions to information-based complexity by a young various group von Neumann algebras are solid. This is a researcher who has not reached his or her thirty-fifth far-reaching generalization of a famous theorem of Ge and birthday by September 30 of the year of the award. The other related results and has been used by many other prize consists of US$1,000 and a plaque. people, who have combined this technique with Popa’s to The award committee this year consisted of Jakob get many very strong results on tensor product decompo- Creutzig, TU Darmstadt; Dirk Nuyens, Katholieke Uni sitions of factors and Cartan subalgebras in factors. Ozawa versiteit, Leuven; Andreas Neuenkirch, University of also has other well-known results on injective operator Frankfurt; Friedrich Pillichshammer, University of Linz; spaces, state spaces of C∗-algebras, and nonexistence of Joseph F. Traub, Columbia University; and Henryk Woznia- a separable universal II1 factor. kowski, Columbia University and University of Warsaw. The Operator Algebra Prize was established in 1999 by initiatives and contributions from some senior Japanese —Joseph Traub, Columbia University researchers in operator algebra theory and related fields to encourage young researchers in these fields. The prize is awarded every four years for outstanding contributions DMV Media Prizes to operator algebra theory and related areas to a person under forty years of age either of Japanese nationality or In November 2008 the Deutsche Mathematiker Vereini- principally based in a Japanese institution. gung (DMV, German Mathematical Society) awarded its media prizes in the Leibniz Room of the Berlin- —Fumio Hiai, Chair, Operator Algebra Prize Committee Brandenburg Academy. The DMV Media Prize went to Christoph Drösser, science journalist and editor for the weekly newspaper Saaty Receives INFORMS Die Zeit. The DMV Journalist Prize was awarded to director and Award author Agnes Handwerk for the radio feature “Geometrie und Revolte” about Alexander Grothendieck. Receiving the Thomas L. Saaty of the University of Pittsburgh has Cartoon Prize for the Year of Mathematics, celebrated in been awarded the 2008 Impact Prize of the Institute Germany in 2008, was the cartoonist known as “kittihawk” for Operations Research and the Management Sciences (http://www.kittihawk.de). (INFORMS). The prize consists of a plaque and a cash award of US$1,000. —Allyn Jackson Saaty was honored for his work in creating the analytic hierarchy process (AHP), a methodology for helping decision makers to make complex, multicriteria decisions. He developed the process based on his work at the U.S. State NSF CAREER Awards Made Department’s Arms Control and Disarmament Agency dur- The Division of Mathematical Sciences (DMS) of the Na- ing the Kennedy and Johnson administrations. He recog- tional Science Foundation (NSF) has honored twenty-three nized that then-current techniques for resolving complex mathematicians in fiscal year 2008 with Faculty Early Ca- decision problems were deficient in both mathematical reer Development (CAREER) awards. The NSF established rigor and relevance to real-world decision making. He the awards to support promising scientists, mathemati- developed key mathematical theories that paired compari- cians, and engineers who are committed to the integration sons with ratio-scale weights to prioritize decision criteria of research and education. The grants provide funding

February 2009 Notices of the AMS 269 Mathematics People of at least US$400,000 over a five-year period. The 2008 logic gates and quantum computational networks; Mark CAREER grant awardees in the mathematical sciences and Kisin of the University of Chicago for his contributions to the titles of their grant projects follow. algebraic number theory; Michael C. Payne of the Univer- Yuri Bakhtin, Georgia Tech Research Corporation, sity of Cambridge for his work in computational physics; Georgia Institute of Technology: Ergodicity and Random Evgeny K. Sklyanin of the University of York for his Media; Scott Baldridge, Louisiana State University contributions to the development of quantum inverse scat- and Agricultural and Mechanical College: The Topology tering techniques and his discoveries concerning the alge- of Smooth and Symplectic 4-Manifolds; Jozsef Balog, braic structure of integrable systems; Ulrike L. Tillmann University of Illinois, Urbana-Champaign: Methods and of Oxford University for her leadership in the study of the Outreach in Modern Combinatorics; Alina Cojocaru, Uni- moduli space of algebraic curves; and David Mumford, versity of Illinois, Chicago: Analytic Problems in Arithmetic emeritus professor at Brown University, who was elected Geometry; Laura DeMarco, University of Illinois, Chi- as a foreign member for his fundamental contributions cago: Algebraic Structures in Complex Dynamics; Math- to algebraic geometry, notably his creation of geometric ias Drton, University of Chicago, Statistical Inference invariant theory and his work on moduli spaces. in Algebraic Models with Singularities; Selim Esedoglu, University of Michigan, Ann Arbor: Analysis and Modeling —From a Royal Society announcement for Image Processing Problems; Dan Geba, University of Rochester: Topics in Nonlinear Wave Equations; David Glickenstein, University of Arizona: Discrete and Gener- Kenneth M. Hoffman alized Riemannian Geometry and Curvature Flows; Shelly Harvey, Rice University: Algebraic Methods in Low- (1930–2008) Dimensional Topology; Demetrio Labate, North Carolina State University: Sparse Directional Multiscale Representa- Kenneth Myron Hoffman, professor emeritus of math- tions: Theory, Implementation, and Applications; Melvin ematics at the Massachusetts Institute of Technology, died Leok, Purdue University: Computational Geometric Me- on September 29, 2008, following a heart attack. He was chanics: Foundations, Computation, and Applications; seventy-seven. He was first appointed instructor at MIT in Yufeng Liu, University of North Carolina, Chapel Hill: Flex- 1956 and C. L. E. Moore Instructor the following year. He ible Statistical Learning for Complex Data; Per-Gunnar joined the mathematics faculty as assistant professor in Martinsson, University of Colorado, Boulder: Fast Direct 1959 (professor in 1964) and retired in 1996 after forty Solvers for Differential and Integral Equations; Govind years of service. Menon, Brown University: Scaling and Self-similarity in Hoffman’s primary area of research specialization was Nonlinear Science Education and Research; Luke Olson, functional analysis. Along with Richard Arens and Isadore University of Illinois, Urbana-Champaign: Multilevel Dis- Singer, he made fundamental contributions to both com- continuous Least-Squares Finite Element Methods; Martin plex and abstract analysis. Some of these appeared in a Olsson, University of California, Berkeley: Stacks, Moduli joint paper with Singer answering many of the questions Spaces, and Log Geometry; Johan Paulsson, Harvard on commutative Banach algebras raised by I. M. Gelfand. University: Fluctuations and Fitness—Fundamental Limits Among his several books was an undergraduate linear and Selection Conflicts; Firas Rassoul-Agha, University algebra textbook, which he wrote jointly with Ray Kunze of Utah: Random Walk in Random Environment; Ben- and which was published in 1961. The book was widely jamin Sudakov, University of California, Los Angeles: used for many decades and became a classic in the field. Methods and Challenges in Discrete Mathematics; Min As head of the MIT mathematics department, Hoffman Yang, University of Missouri, Columbia: Optimal Design oversaw crucial faculty appointments and developed the of Experiments for Generalized Linear Models; Wotao undergraduate faculty chair position. He crafted an affir- Yin, Rice University: Optimizations for Sparse Solutions mative action plan that was modeled elsewhere. and Applications; Ji Zhu, University of Michigan, Ann In 1980 Hoffman moved to Washington, D.C., where Arbor: Statistical Learning from Data with Graph/Network over the next ten years he worked to raise understand- Structures. ing of the central role of mathematics in science. Among other leadership positions, he served as executive direc- —Elaine Kehoe tor of the Committee on Resources for the Mathematical Sciences of the National Research Council (1981–84). The committee’s 1984 report, nicknamed the “David Report”, highlighted the imbalance between research support for Royal Society of London the mathematical sciences and related disciplines in sci- Elections ence and engineering. During the same period, Hoffman chaired the Committee on Science Policy of the AMS and in The Royal Society of London has elected forty-four new 1984–85 chaired the Advisory Committee for Science and fellows and foreign associates for 2008. Among them are Engineering Education at the National Science Foundation. six whose work involves the mathematical sciences. They From 1984 to 1989 he headed the Office of Governmental are: David E. Deutsch of Oxford University for his work in and Public Affairs of the Joint Policy Board for Mathemat- quantum theory of computation, including the discovery ics, which successfully worked to implement the recom- of the first quantum algorithms and the theory of quantum mendations of the David Report.

270 Notices of the AMS Volume 56, Number 2 Mathematics People

For his extensive service and leadership, Hoffman was brought out the first issue of the FOCUS newsletter. She selected as the inaugural recipient of two national service served as editor of FOCUS until September 1985, when awards in mathematics: the Public Service Award of the she left the MAA. Joint Policy Board for Mathematics (1986) and the first She then became executive director of the MSEB, which AMS Award for Distinguished Public Service (1990). The was established by the NRC in response to the “David citation for the latter award reads in part: “Through his Report”, Renewing U.S. Mathematics: Critical Resource efforts, the awareness of the importance of mathematics for the Future. She convened a stellar advisory board and and the support of mathematical research has been sig- raised sufficient funds to see the MSEB grow enormously in nificantly heightened in the general public, among makers influence. The board’s seminal report, Everybody Counts: of science policy in the government, and among university A Report to the Nation on the Future of Mathematics administrators.” Education, remains to this day a key resource for K–12 Born in Long Beach, California, Hoffman earned a mathematics education. bachelor’s degree in mathematics from Occidental Col- Sward returned to lead the MAA in 1989 on the occasion lege in 1952. He received an M.A. (1954) and Ph.D. (1956) of the retirement of Alfred Willcox. Under her leadership, in mathematics from the University of California, Los the MAA increased its membership, programs, and rev- Angeles. enue. She was instrumental in initiating new programs, including the highly successful Project NExT and SUMMA —From an MIT news release (Supporting Undergraduate Minority Mathematics Achieve- ment). She retired from the MAA in 1999 but continued her association with the MAA, regularly participating in Marcia P. Sward the winter meetings, special events at the Carriage House, and MAA study tours. (1939–2008) —Based an article in MAA FOCUS by Linda P. Rosen Marcia Peterson Sward died on September 21, 2008, from kidney cancer that was diagnosed just weeks before her death. Sward served as the first associate executive director of the Mathematical Association of America (MAA) between Correction 1980 and 1985. She returned to the MAA as executive director in 1989. Between her two periods at the MAA, The January 2009 issue of the Notices carried an ar- she served as the executive director of the Mathematical ticle about the retirement of AMS executive director Sciences Education Board (MSEB) at the National Research John Ewing. Accompanying the article was a sidebar by Council (NRC) of the National Academy of Sciences. Jonathan Borwein, the byline of which mistakenly gave “You face all sorts of problems in a large association Borwein’s affiliation as the University of British Columbia. like the MAA, brought to you by all sorts of people,” said He has been on the faculty of Dalhousie University since AMS executive director John Ewing. “Marcia was the con- 2004; prior to that he was at Simon Fraser University in summate professional in dealing with both problems and Vancouver. The Notices regrets the error. people—always gracious and thoughtful. It was always a pleasure working alongside her when the AMS and MAA —Allyn Jackson worked together.” Because the AMS Washington Office is right next door to the MAA, Washington Office director Samuel M. Rankin III got to know Sward well. “I remember Marcia as being very focused on improving mathematics education and being a dedicated leader of MAA,” he remarked. Marcia Sward graduated summa cum laude and first in her class at Vassar College with a degree in mathematics. Under the direction of Edward Scott, she was awarded her Ph.D. in 1967 for her dissertation “The Mixed Boundary Value Problem along the Line of Parabolicity for a Certain Class of Hyperbolic Partial Differential Equations”. After graduation she spent a year at Catholic Univer- sity in Washington, D.C., before beginning her academic career at Trinity College, also in Washington, D.C. After a one-year visiting appointment at the National Highway Traffic Safety Administration, she accepted a newly created position as associate executive director of the MAA. The position included, among other tasks, directing publication of the organization’s three journals and creating a newsletter to serve members’ needs. In March 1981 she

February 2009 Notices of the AMS 271 Mathematics Opportunities

Participants can also enjoy the simpler pleasures of Mathematics Research convening on the patios at the resort to read, work, and Communities 2009 socialize. In the evenings colleagues enjoy informal gatherings The American Mathematical Society (AMS) invites math- to network and continue discussion of the day’s sessions ematicians just beginning their research careers to be- over refreshments. Within a half hour of the University come part of Mathematics Research Communities, a new of Utah, Snowbird is easily accessible from the Salt Lake program to develop and sustain long-lasting cohorts for City International Airport. For more information about collaborative research projects in many areas of math- Snowbird Resort, see http://www.snowbird.com. ematics. Women and underrepresented minorities are A report about the 2008 MRC conferences appears in especially encouraged to participate. The AMS will provide this issue of the Notices. For information on applying for a structured program to engage and guide all participants the 2009 program, please visit the website http://www. as they start their careers. The program will include: a one- ams.org/amsmtgs/mrc-09.html. For further information week summer conference for each topic, special sessions about the MRC program, please contact AMS associate at the national meeting, discussion networks by research executive director Ellen Maycock at [email protected]. topic, ongoing mentoring, and a longitudinal study of early career mathematicians. —AMS announcement The summer conferences of the Mathematics Research Communities will be held in Snowbird Resort, Utah, where participants can enjoy the natural beauty and a collegial NSF Program ADVANCE atmosphere. The application deadline for summer 2009 is March 2, 2009. This program is supported by a grant The National Science Foundation (NSF) has instituted the from the National Science Foundation. Advanced gradu- ADVANCE Program in an effort to increase the representa- ate students and postdoctoral researchers are welcome to tion and advancement of women in academic science and apply to be participants. engineering careers. The topics, dates, and organizers of the 2009 confer- In 2009 this program will support three types of proj- ences follow. ects. Partnerships for Adaptation, Implementation, and Mathematical Challenges of Relativity, June 13–19, Dissemination (PAID) awards support analysis, adaptation, 2009, Mihalis Dafermos (University of Cambridge), Alex- dissemination, and use of existing innovative materials andru Ionescu (University of Wisconsin, Madison), Sergiu and practices that have been demonstrated to be effective Klainerman (Princeton University, chair), and Richard in increasing representation and participation of women in Schoen (Stanford University). academic science and engineering careers. This category Inverse Problems, June 20–26, 2009, Guillaume Bal of award also supports scientific research designed to (Columbia University), Allan Greenleaf (University of advance understanding of gender in academic science and Rochester), Todd Quinto (Tufts University), and Gunther engineering careers. The deadline for required letters of Uhlmann (University of Washington, chair). intent is January 20, 2009; the deadline for full proposals Modern Markov Chains and Their Statistical Applica- is February 24, 2009. tions, June 27–July 3, 2009, Persi Diaconis (Stanford Institutional Transformation (IT) awards support University, chair), Jim Hobert (University of Florida), and academic institutional transformation to promote the Susan Holmes (Stanford University). increased participation and advancement of women sci- Harmonic Analysis, June 27–July 3, 2009, Ciprian De- entists and engineers in academe. These awards support meter (Indiana University), Michael Lacey (Georgia Insti- innovative and comprehensive programs for institution- tute of Technology), and Christoph Thiele (University of wide change. The deadline for letters of intent for these California, Los Angeles, chair). awards is August 4, 2009; the full proposal deadline is Situated in a breathtakingly beautiful mountain setting, November 12, 2009. Snowbird Resort provides an extraordinary environment Institutional Transformation Catalyst (IT-Catalyst) for the MRC. The atmosphere is comparable to the col- awards are designed to support institutional self- legial gatherings at Oberwolfach and other conferences assessment activities, such as basic data collection and that combine peaceful natural ambience with stimulating analysis and policy review, in order to identify specific is- meetings. sues in the recruitment, retention, and promotion of women MRC participants have access to a range of activities, faculty in institutions of higher education. The deadline for such as a tram ride to the top of the mountain, guided letters of intent for these awards is August 4, 2009, and the hikes, swimming, mountain bike tours, rock climbing, plus full proposal deadline is November 12, 2009. heated outdoor pools. More than a dozen walking and Proposals are sought from both men and women for hiking trails head deep into the surrounding mountains. creative strategies to realize the goals of the ADVANCE

272 Notices of the AMS Volume 56, Number 2 Mathematics Opportunities

Program. Members of underrepresented minority groups and a stipend of US$1,750. The deadline for applications and individuals with disabilities are especially encouraged is February 27, 2009. Early applications are encouraged. to apply. Proposals that address the participation and Applications are accepted only by mail. For further in- advancement of women with disabilities and women from formation, please contact the director, Murli M. Gupta, underrepresented minority groups are encouraged. For email: [email protected], telephone: 202-994-4857; or visit more information see http://www.nsf.gov/pubs/2009/ the program’s website at http://www.gwu.edu/~spwm/. nsf09504/nsf09504.htm. Application material is available on the website.

—From an NSF announcement —From an SPWM announcement NSF Partnerships for NSF Support for International Research and Undergraduate Training in Education Biological and Mathematical The National Science Foundation (NSF) has instituted Sciences the Partnerships for International Research and Educa- tion (PIRE) program to support innovative international The National Science Foundation (NSF) offers opportuni- research and education collaborations. The program will ties for support through its Undergraduate Biology and enable U.S. scientists and engineers to establish collabora- Mathematics (UBM) program. The goal of the program is tive relationships with international colleagues to advance to enhance undergraduate education and training at the knowledge and scientific discoveries and to promote the intersection of the biological and mathematical sciences development of a diverse, globally engaged U.S. scientific and to better prepare undergraduate biology or mathemat- and engineering workforce. The program aims to sup- ics students to pursue graduate study and careers in fields port partnerships that will strengthen the capacity of that integrate the mathematical and biological sciences. institutions, multi-institutional consortia, and networks The program will provide support for jointly conducted to engage in and benefit from international research and long-term research experiences for interdisciplinary- education collaborations. balanced teams of at least two undergraduates from de- Proposals may involve one or more disciplines, U.S. partments in the biological and the mathematical sciences. institutions, foreign institutions, and countries. The dead- Projects should focus on research at the intersection of line for preliminary proposals is February 26, 2009. Full the mathematical and biological sciences and should proposals may be submitted by invitation only; the dead- provide students exposure to contemporary mathematics line for these is August 4, 2009. For complete informa- and biology addressed with modern research tools and tion see http://www.nsf.gov/pubs/2009/nsf09505/ methods. Projects must involve students from both areas nsf09505.htm. in collaborative research experiences and include joint mentorship by faculty in both fields. —From an NSF announcement Between six and nine awards are expected to be made in 2009. The deadline for full proposals is February 12, 2009. For more information see http://www.nsf.gov/ Summer Program for Women pubs/2008/nsf08510/nsf08510.htm. The UBM program is a joint effort of the Education and Human Resources Undergraduates (EHR), Biological Sciences (BIO), and Mathematical and The 2009 Summer Program for Women in Mathematics Physical Sciences (MPS) directorates of the NSF. (SPWM2009) will take place at George Washington Univer- sity in Washington, D.C., from June 27 to August 1, 2009. —From an NSF announcement This is a five-week intensive program for mathematically talented undergraduate women who are completing their junior years and may be contemplating graduate study in Nominations for Information- mathematical sciences. The goals of this program are to communicate an enthusiasm for mathematics, to develop Based Complexity Prize 2009 research skills, to cultivate mathematical self-confidence The annual Prize for Achievement in Information-Based and independence, and to promote success in graduate Complexity consists of US$3000 and a plaque, and will be school. awarded at a suitable location. Nominations may be sent to Applicants must be U.S. citizens or permanent residents Joseph Traub, [email protected]. The deadline for studying at a U.S. university or college who are completing nominations is March 31, 2009. The award can be based their junior years or the equivalent and have mathemati- on work done in a single year, in a number of years, or cal experience beyond the typical first courses in calculus over a lifetime. and linear algebra. Sixteen women will be selected. Each will receive a travel allowance, campus room and board, —Joseph Traub, Columbia University

February 2009 Notices of the AMS 273 Inside the AMS

Night”; Donald Saari (University of California, Irvine) and From the AMS Public John Allen Paulos (Temple University), explaining aspects Awareness Office of mathematics and voting; Oded Schramm, a member of the Theory Group at Microsoft Research, who died in •Arnold Ross Lecture by David Kelly. David Kelly a tragic hiking accident; Donald Clayton Spencer, who (Hampshire College) gave his lecture From Pascal’s Tri- had a mountain peak in Colorado named after him; and angle to Sierpinski’s Triangle in Base 2 to over one hundred Manil Suri (University of Maryland Baltimore County), enthusiastic students at who also writes novels. Find these and other mathemati- the Oregon Museum of cians quoted in newspapers and interviewed on radio in Science and Industry the 2008 Math Digest archive at http://www.ams.org/ (OMSI) in late October. mathmedia/mathdigest/md-2008-toc.html. Arnold Ross (1906–2002) started a mathematics —Annette Emerson and Mike Breen enrichment program AMS Public Awareness Officers for high school teach- [email protected] ers in 1947. He started his multi-level summer program for gifted high AMS Email Support for school students in 1957 and ran it every sum- Frequently Asked Questions mer until 2000, giving the number theory lec- A number of email addresses have been established for ture each morning. In contacting the AMS staff regarding frequently asked ques- keeping with this presti- tions. The following is a list of those addresses together gious tradition, the AMS with a description of the types of inquiries that should be David Kelly presents a lecture for made through each address. talented high school [email protected] for questions regarding a particular mathematics students each year to stimulate their inter- abstract. est in mathematics beyond the traditional classroom and [email protected] for information on how to submit to show them the tremendous opportunities for careers in abstracts for AMS meetings and MAA sessions at January mathematics—as mathematics teachers and as researchers Joint Mathematics Meetings. Type HELP as the subject in government, industry, and university programs. The line. 2009 lecture will be held at the National Science Center in [email protected] to contact the AMS Acquisitions Augusta, Georgia. Read about the 2008 lecture and Who Department. Wants to Be a Mathematician that immediately followed [email protected] to contact the Society’s headquarters in at http://www.ams.org/wwtbam/archive/arl2008. Providence, Rhode Island. html. [email protected] to contact the Society’s office in Washington, D.C. Feature Column. Recent columns include “From • [email protected] to request information about mem- Bézier to Bernstein”, by Bill Casselman, “Inside-out bership in the AMS and about dues payments or to ask Frieze Symmetries in Ancient Peruvian Weavings”, by Tony any general membership questions; may also be used to Phillips, “Gray Codes”, by Joe Malkevitch, and “Percola- submit address changes. tion: Slipping through the Cracks”, by David Austin, at [email protected] for information or questions http://www.ams.org/featurecolumn/. about the Annual Survey of the Mathematical Sciences or •Mathematicians in the media over the past few to request reprints of survey reports. months include Jason Brown (Dalhousie University) for [email protected] for inquiries related to the online work he did analyzing the opening chord of “A Hard Day’s AMS Bookstore.

274 Notices of the AMS Volume 56, Number 2 Inside the AMS

[email protected] to submit classified advertising for electronically submit accepted manuscripts to the AMS the Notices. book and journal programs. [email protected] for general information about AMS [email protected] to request permission to products (including electronic products), to send address reprint material from Society publications. changes, place credit card orders for AMS products, or [email protected] to inquire about reselling or distributing conduct any general correspondence with the Society’s AMS publications or to send correspondence to the AMS Customer Services Department. Sales Department. [email protected] for information about giving [email protected] to contact the secretary of the to the AMS, including the Epsilon Fund. Society. [email protected] to request general information [email protected] to correspond regarding a bal- about Employment Information in the Mathematical Sci- ance due shown on a monthly statement. ences (EIMS). For ad deadlines and rates go to http:// [email protected] to contact the Society’s typeset- www.ams.org/eims. ting Technical Support Group. [email protected] for information regarding AMS [email protected] to request examination copies or employment and career services. inquire about using AMS publications as course texts. [email protected] for technical questions re- [email protected] for general information or for garding AMS electronic products and services. assistance is accessing and using the AMS website. [email protected] to send information to be included in the “Mathematics Calendar” section of the Notices. [email protected] to submit reviews to Mathematical Deaths of AMS Members Reviews and to send correspondence related to reviews or other editorial questions. Antonio Aizpuru, professor, University of Cadiz, Spain, [email protected] to request general information about died on March 1, 2008. Born on September 13, 1954, he was Society meetings and conferences. a member of the Society for 10 years. [email protected] to request email meeting Jack M. Anderson, retired, from Hill City, SD, died on registration forms. August 18, 2008. Born on June 13, 1937, he was a member [email protected] to submit completed regis- of the Society for 14 years. tration forms. David Gottlieb, professor, Brown University, died on [email protected] for information or questions about December 6, 2008. Born on November 14, 1944, he was a registration and housing for the Joint Mathematics Meet- member of the Society for 19 years. ings (Mathematics Meetings Service Bureau). Craciun Iancu, associate professor, University of [email protected] for technical questions regard- Cluj-Napoca, Romania, died on March 12, 2007. Born on ing MathSciNet. September 15, 1939, he was a member of the Society for [email protected] to send correspondence to the 15 years. managing editor of the Notices, including items for the Kiyoshi Ito, from Kyoto-shi, Japan, died on Novem‑ news columns. The editor ([email protected]) is the ber 10, 2008. Born on September 7, 1915, he was a member person to whom to send articles and letters. Requests for of the Society for 47 years. permission to reprint from the Notices should be sent to Hendrik S. Konijn, professor emeritus, University of [email protected] (see below). California, Berkeley, died on October 14, 2008. Born on [email protected] to submit electronically paid March 17, 1918, he was a member of the Society for 61 display ads for the Notices. (Hard copy of the ad should years. also be faxed or sent via postal mail.) William Light, professor, University of Leicester, Eng- [email protected] to submit suggestions for land, died on December 8, 2002. Born on April 19, 1950, books to be included in the “Book List” in the Notices. he was a member of the Society for 17 years. [email protected] to submit letters and opinion pieces to the Notices. David Middleton, from New York, NY, died on Novem- [email protected] to comment on or send sug- ber 16, 2008. Born on April 19, 1920, he was a member of gestions for topics for the “WHAT IS…?” column in the the Society for 37 years. Notices. Katsumi Nomizu, professor emeritus, Brown University, [email protected] to contact the AMS Public Aware- died on November 5, 2008. Born on December 1, 1924, he ness Office. was a member of the Society for 57 years. [email protected] to contact the president of the George Pimbley, retired, from Los Alamos, NM, died on American Mathematical Society. August 14, 2008. Born on March 11, 1922, he was a member [email protected] to send correspondence about AMS of the Society for 50 years. professional programs and services. Robert H. Smith, from Woodbury, NJ, died on July 31, [email protected] to send correspondence to the AMS 2008. Born on March 7, 1943, he was a member of the Publication Division. Society for 2 years. [email protected] to submit accepted electronic Susan Williamson, from Newton Centre, MA, died manuscripts to AMS publications (other than Abstracts). on July 26, 2008. Born on December 29, 1936, she was See http://www.ams.org/submit-book-journal to a member of the Society for 41 years.

February 2009 Notices of the AMS 275 Reference and Book List

The Reference section of the Notices Selected Professions Fellowships, Manager, Mass Media Program, AAAS is intended to provide the reader Dept. 60, 301 ACT Drive, Iowa City, Mass Media Science and Engineering with frequently sought information in IA 52243-4030; telephone: 319-337- Fellows Program, 1200 New York an easily accessible manner. New 1716, ext. 60; email: [email protected]. Avenue, NW, Washington, DC 20005; information is printed as it becomes January 15, 2009: Applications telephone: 202-326-6441; fax: 202- available and is referenced after the for Jefferson Science Program at U.S. 371-9849; email: [email protected]. first printing. As soon as information Department of State. See http:// Also see http://www.ams.org/ is updated or otherwise changed, it www7.nationalacademies.org/ government/massmediaann.html will be noted in this section. jefferson/; telephone: 202-334- or contact the AMS Washington Of- 2643; email: [email protected]. fice, 1527 Eighteenth Street, NW, Contacting the Notices January 15, 2009: Applications Washington, DC 20036; telephone: The preferred method for contacting for AMS-AAAS Mass Media Sum- 202-588-1100; fax: 202-588-1853; the Notices is electronic mail. The mer Fellowships. See http://www. email: [email protected]. editor is the person to whom to send aaas.org/programs/education/ January 18, 2009: Applications for articles and letters for consideration. MassMedia/; or contact Stacey Pasco, Mathematical Biosciences Institute Articles include feature articles, memorial articles, communications, opinion pieces, and book reviews. Where to Find It The editor is also the person to whom A brief index to information that appears in this and previous issues of the Notices. to send news of unusual interest AMS Bylaws—November 2007, p. 1366 about other people’s mathematics AMS Email Addresses—February 2009, p. 274 research. AMS Ethical Guidelines—June/July 2006, p. 701 The managing editor is the person AMS Officers 2006 and 2007 Updates—May 2008, p. 629 to whom to send items for “Math- ematics People”, “Mathematics Op- AMS Officers and Committee Members—October 2008, p. 1122 portunities”, “For Your Information”, Conference Board of the Mathematical Sciences—September 2008, “Reference and Book List”, and “Math- p. 980 ematics Calendar”. Requests for IMU Executive Committee—December 2008, p. 1441 permissions, as well as all other Information for Notices Authors—June/July 2008, p. 723 inquiries, go to the managing editor. Mathematics Research Institutes Contact Information—August 2008, The electronic-mail addresses are p. 844 [email protected] in the case of National Science Board—January 2009, p. 67 the editor and [email protected] in New Journals for 2006, 2007—June/July 2008, p. 725 the case of the managing editor. The fax numbers are 405-325-7484 for NRC Board on Mathematical Sciences and Their Applications—March the editor and 401-331-3842 for the 2008, p. 401 managing editor. Postal addresses NRC Mathematical Sciences Education Board—April 2008, p. 515 may be found in the masthead. NSF Mathematical and Physical Sciences Advisory Committee—February 2009, p. 278 Upcoming Deadlines Program Officers for Federal Funding Agencies—October 2008, January 10, 2009: Applications for p. 1116 (DoD, DoE); December 2007, p. 1359 (NSF); December 2008, AAUW Educational Foundation Fel- p. 1440 (NSF Mathematics Education) lowships and Grants. See http:// Program Officers for NSF Division of Mathematical Sciences— www.aauw.org/fga/fellowships_ November 2008, p. 1297 grants/selected.cfm or contact Stipends for Study and Travel—September 2008, p. 983 the AAUW Educational Foundation,

276 Notices of the AMS Volume 56, Number 2 Reference and Book List

(MBI) Early Career Visitor and post- tation, and Dissemination (PAID) May 8, 2009: Applications for AWM doctoral positions. See the website awards. See “Mathematics Opportuni- Travel Grants. See http://www.awm- http://mbi.osu.edu or call 614- ties” in this issue. math.org/travelgrants.html; 292-3648. February 26, 2009: Preliminary telephone: 703-934-0163; email: awm@ January 20, 2009: Letters of intent proposals for NSF Partnerships for awm-math.edu. The postal address is: for NSF Program ADVANCE Part- International Research and Education Association for Women in Mathemat- nerships for Adaptation, Implemen- (PIRE). See “Mathematics Opportuni- ics, 11240 Waples Mill Road, Suite tation, and Dissemination (PAID) ties” in this issue. 200, Fairfax, VA 22030. awards. See “Mathematics Opportuni- February 27, 2009: Applica- May 15, 2009: Applications for ties” in this issue. tions for 2009 Summer Program for National Academies Research Associ- January 22, 2009: Proposals for Women in Mathematics (SPWM2009). ateship Programs. See http://www7. NSF Scientific Computing Research See “Mathematics Opportunities” in nationalacademies.org/rap/ or Environments for the Mathemati- this issue. contact Research Associateship Pro- cal Sciences (SCREMS). See http:// February 27, 2009: Submis- grams, National Research Council, www.nsf.gov/funding/pgm_summ. sions for Association for Women in Keck 568, 500 Fifth Street, NW, Wash- jsp?pims_id=5616. Mathematics (AWM) essay contest. ington, DC 20001; telephone 202- January 31, 2009: Applications See http://www.awm-math.org/ 334-2760; fax 202-334-2759; email: for AMS-AAAS Congressional Fel- biographies/contest.html. [email protected]. lowship. See http://www.ams.org/ February 27, 2009: Proposals for June 1, 2009: Applications for government/congressfellowann. DMS New Institute Competition. See the September program of the Chris- html or contact the AMS Washing- http://www.nsf.gov/funding/ tine Mirzayan Science and Technol- ton Office at 202-588-1100, email: pgm_summ.jsp?pims_id=5302. ogy Policy Graduate Fellowship Pro- [email protected]. March 1, 2009: Applications for gram of the National Academies. See February 1, 2009: Applications the June program of the Christine http://www7.nationalacademies. for AWM Travel Grants. See http:// org/policyfellows; or contact The Mirzayan Science and Technology www.awm-math.org/travelgrants. National Academies Christine Mirza- Policy Graduate Fellowship Pro- html; telephone: 703-934-0163; email: yan Science and Technology Policy gram of the National Academies. See [email protected]. The postal ad- Graduate Fellowship Program, 500 http://www7.nationalacademies. dress is: Association for Women in Fifth Street, NW, Room 508, Wash- org/policyfellows; or contact The Mathematics, 11240 Waples Mill ington, DC 20001; telephone: 202- National Academies Christine Mirza- Road, Suite 200, Fairfax, VA 22030. 334-2455; fax: 202-334-1667; email: yan Science and Technology Policy February 12, 2009: Full propos- [email protected]. Graduate Fellowship Program, 500 als for NSF Undergraduate Biology June 1, 2009: Applications for the Fifth Street, NW, Room 508, Wash- and Mathematics (UBM) program. Math for America Foundation (MfA) ington, DC 20001; telephone: 202- See “Mathematics Opportunities” in Fellowship Program in San Diego. 334-2455; fax: 202-334-1667; email: this issue. See http://www.mathforamerica. [email protected] February 13, 2009: Applica- . org/. tions for Math for America Foun- March 2, 2009: Applications for June 2, 2009: Proposals for NSF’s dation (MfA) Fellowship Program EDGE Summer Program. See http:// Enhancing the Mathematical Sci- for New York City and Los Angeles. www.edgeforwomen.org/?page_ ences Workforce in the Twenty-First See http://www.mathforamerica. id=5. Century program. See http://www. org/. March 31, 2009: Submissions for nsf.gov/publications/pub_summ. February 15, 2009: Applications Plus Magazine New Writers Award. See jsp?ods_key=nsf05595. for National Academies Research the website http://plus.maths. June 30, 2009: Applications for Associateship Programs. See http:// org/competition/. Fermat Prize for Mathematics Re- www7.nationalacademies.org/ April 15, 2009: Applications for search. Contact Prix Fermat de Re- rap/ or contact Research Associate- fall 2009 semester of Math in Mos- cherche en Mathématiques, Service ship Programs, National Research cow. See http://www.mccme.ru/ Relations Publiques, Université Paul Council, Keck 568, 500 Fifth Street, mathinmoscow or write to: Math in Sabatier, 31062 Toulouse Cedex 9, NW, Washington, DC 20001; tele- Moscow, P.O. Box 524, Wynnewood, PA France, or see the website http:// phone 202-334-2760; fax 202-334- 19096; fax: +7095-291-65-01; email: www.math.ups-tlse.fr/Fermat/. 2759; email: [email protected]. [email protected]. For information on August 4, 2009: Letters of intent February 15, 2009: Nominations AMS scholarships see http://www. for NSF Project ADVANCE Institu- for Clay Liftoff Program for sum- ams.org/outreach/mimoscow.html tional Transformation (IT) and Insti- mer 2009. See http://claymath. or write to: Math in Moscow Program, tutional Transformation Catalyst (IT- org/fas/liftoff; telephone: 617- Membership and Programs Depart- Catalyst) awards. See “Mathematics 995-2600. ment, American Mathematical Soci- Opportunities” in this issue. February 24, 2009: Full propos- ety, 201 Charles Street, Providence RI August 4, 2009: Full proposals als for NSF Project ADVANCE Part- 02904-2294; email: student-serv@ (by invitation only) for NSF Partner- nerships for Adaptation, Implemen- ams.org. ships for International Research and

February 2009 Notices of the AMS 277 Reference and Book List

Education (PIRE). See “Mathematics may be found at http://www.nsf. Sharon L. Neal (10/11) Opportunities” in this issue. gov/home/mps/. The postal address Department of Chemistry August 15, 2009: Applications for is Directorate for the Mathematical and Biochemistry National Academies Research Associ- and Physical Sciences, National Sci- University of Delaware ateship Programs. See http://www7. ence Foundation, 4201 Wilson Bou- Monica Olvera de la Cruz (10/09) nationalacademies.org/rap/ or levard, Arlington, VA 22230. Department of Materials Science contact Research Associateship Pro- and Engineering grams, National Research Council, Hector D. Abruna (10/10) Northwestern University Keck 568, 500 Fifth Street, NW, Wash- Department of Chemistry ington, DC 20001; telephone 202- John Peoples Jr. (10/11) and Chemical Biology 334-2760; fax 202-334-2759; email: Fermilab Batavia, IL Cornell University [email protected]. Elsa Reichmanis (10/11) October 1, 2009: Applications for James Berger (10/11) Georgia Institute of Technology AWM Travel Grants. See http:// Department of Statistical Science Ian M. Robertson (10/09) www.awm-math.org/travelgrants. Duke University Department of Materials Science html; telephone: 703-934-0163; email: Daniela Bortoletto (10/11) and Engineering [email protected]. The postal ad- Department of Physics University of Illinois, dress is: Association for Women in Purdue University Urbana-Champaign Mathematics, 11240 Waples Mill Road, Suite 200, Fairfax, VA 22030. Eric A. Cornell (10/10) Winston O. Soboyejo (10/09) November 1, 2009: Applications JILA University of Colorado Department of Mechanical for the January program of the Chris- Barbara J. Finlayson-Pitts (10/11) and Aerospace Engineering tine Mirzayan Science and Technol- Department of Chemistry Princeton University ogy Policy Graduate Fellowship Pro- University of California, Irvine Joel E. Tohline (10/10) gram of the National Academies. See Irene Fonseca (10/11) Department of Physics http://www7.nationalacademies. Department of Mathematical Sciences and Astronomy org/policyfellows; or contact The Carnegie Mellon University Louisiana State University National Academies Christine Mirza- yan Science and Technology Policy Suzanne Hawley (10/11) Geoffrey West (10/11) Graduate Fellowship Program, 500 University of Washington Santa Fe Institute Santa Fe, NM Fifth Street, NW, Room 508, Wash- Iain M. Johnstone (chair) (10/09) Robert Williams (10/09) ington, DC 20001; telephone: 202- Department of Statistics Space Telescope Science Institute 334-2455; fax: 202-334-1667; email: Stanford University Baltimore, MD [email protected]. November 12, 2009: Full pro- William L. Jorgensen (10/09) Book List posals for NSF Project ADVANCE Department of Chemistry The Book List highlights books that Institutional Transformation (IT) and Yale University have mathematical themes and are Institutional Transformation Catalyst David E. Keyes (10/09) aimed at a broad audience potentially (IT-Catalyst) awards. See “Mathemat- Department of Applied Physics including mathematicians, students, ics Opportunities” in this issue. and Applied Mathematics and the general public. When a book November 15, 2009: Applications Columbia University has been reviewed in the Notices, a for National Academies Research As- reference is given to the review. Gen- sociateship Programs. See http:// Theresa A. Maldonado erally the list will contain only books www7.nationalacademies.org/ (MPSAC/CEOSE Liaison) (10/09) published within the last two years, rap/ or contact Research Associate- Department of Electrical though exceptions may be made in ship Programs, National Research and Computer Engineering cases where current events (e.g., the Council, Keck 568, 500 Fifth Street, Texas A&M University death of a prominent mathematician, NW, Washington, DC 20001; tele- Dennis L. Matthews (10/10) coverage of a certain piece of math- phone 202-334-2760; fax 202-334- College of Engineering ematics in the news) warrant drawing 2759; email: [email protected]. and School of Medicine readers’ attention to older books. Sug- University of California Davis gestions for books to include on the list NSF/MPS Advisory Committee may be sent to notices-booklist@ Dusa M. McDuff (10/09) Following are the names and affilia- ams.org. Department of Mathematics tions of the members of the Advisory *Added to “Book List” since the State University of New York, Committee for Mathematical and list’s last appearance. Stony Brook Physical Sciences (MPS) of the Na- tional Science Foundation. The date Ramesh Narayan (10/11) An Abundance of Katherines, by of the expiration of each member’s Harvard University John Green. Dutton Juvenile Books, term is given after his or her name. and Harvard-Smithsonian Center September 2006. ISBN-13:978-0-5254- The website for the MPS directorate for Astrophysics 7688-7. (Reviewed October 2008.)

278 Notices of the AMS Volume 56, Number 2 Reference and Book List

Amongst Mathematicians: Teach- *Fifty Mathematical Ideas You Re- The Indian Clerk, by David Leavitt. ing and Learning Mathematics at ally Need to Know, by Tony Crilly. Bloomsbury USA, September 2007. University Level, by Elena Nardi. Quercus, 2007. ISBN-13: 978-18472- ISBN-13: 978-15969-1040-9. (Reviewed Springer, November 2007. ISBN-13: 400-88. September 2008.) 978-0-387-37141-2. Fighting Terror Online: The Con- Irreligion: A Mathematician Ex- *The Annotated Turing: A Guided vergence of Security, Technology and plains Why the Arguments for God Tour Through Alan Turing’s His- the Law, by Martin Charles Golum- Just Don’t Add Up, by John Allen toric Paper on Computability and bic. Springer, 2008. ISBN: 978-0-387- Paulos. Hill and Wang, December the Turing Machine, by Charles Pet- 73577-1. 2007. ISBN-13: 978-0-8090-591-95. zold. Wiley, June 2008. ISBN-13: 978- Five-Minute Mathematics, by (Reviewed August 2008.) 04702-290-57. Ehrhard Behrends (translated by Is God a Mathematician? by Mario The Archimedes Codex, by Reviel David Kramer). AMS, May 2008. ISBN- Livio. Simon & Schuster, January Netz and William Noel. Weidenfeld 13: 978-08218-434-82. 2009. ISBN-13: 978-07432-940-58. and Nicolson, May 2007. ISBN-13: Fly Me to the Moon: An Insider’s Kiss My Math: Showing Pre-Algebra 978-0-29764-547-4. (Reviewed Sep- Guide to the New Science of Space Who’s Boss, by Danica McKellar. Hud- tember 2008.) Travel, by Edward Belbruno. Prince son Street Press, August 2008. ISBN-13: The Book of Numbers: The Secret ton University Press, January 2007. 978-1594630491. of Numbers and How They Changed ISBN-13: 978-0-6911-2822-1. (Re- The Last Theorem, by Arthur C. the World, by Peter J. Bentley. Firefly viewed April 2008.) Clarke and Frederik Pohl. Del Rey, Au- Books, February 2008. ISBN-13: 978- Geekspeak: How Life + Mathemat- gust 2008. ISBN-13: 978-0345470218. 15540-736-10. ics = Happiness, by Graham Tattersall. Leonhard Euler, A Man to Be Reck- The Cat in Numberland, by Ivar Collins, September 2008. ISBN-13: oned With, by Andreas K. Heyne and Ekeland. Cricket Books, April 2006. 978-00616-292-42. Alice K. Heyne. Birkhäuser, 2007. ISBN- ISBN-13: 978-0-812-62744-2. (Re- Geometric Folding Algorithms: 13: 978-3-7643-8332-9. (Reviewed viewed January 2009.) Linkages, Origami, Polyhedra, by March 2008.) Digital Dice, by Paul J. Nahin. Princ- Erik D. Demaine and Joseph O’Rourke. Logic’s Lost Genius: The Life of eton University Press, March 2008. Cambridge University Press, July Gerhard Gentzen, by Eckart Menzler- ISBN-13: 978-06911-269-82. 2007. ISBN-13: 978-05218-57574. Trott, Craig Smorynski (translator), Dimensions, by Jos Leys, Etienne *Geometric Origami, by Robert Edward R. Griffor (translator). AMS- Ghys, and Aurélien Alvarez. DVD, 117 Geretschläger. Arbelos, October 2008. LMS, November 2007. ISBN-13: 978-0- minutes. Available at http://www. ISBN-13: 978-09555-477-13. 8218-3550-0. dimensions-math.org. The Golden Section: Nature’s Great- Making Mathematics Work with Discovering Patterns in Mathemat- est Secret (Wooden Books), by Scott Needlework: Ten Papers and Ten ics and Poetry, by Marcia Birken and Olsen. Walker and Company, October Projects, edited by Sarah-Marie Bel- Anne C. Coon. Rodopi, February 2008. 2006. ISBN-13: 978-08027-153-95. castro and Carolyn Yackel. A K Peters, ISBN-13: 978-9-0420-2370-3. Group Theory in the Bedroom, and September 2007. ISBN-13: 978-1-5688- Does Measurement Measure Up?: Other Mathematical Diversions, by 1331-8. How Numbers Reveal and Conceal Brian Hayes. Hill and Wang, April 2008. The Map of My Life, by Goro the Truth, by John Henshaw. Johns ISBN-13: 978-08090-521-96. (Reviewed Shimura. Springer, September 2008. Hopkins University Press, March 2006. in this issue.) ISBN-13: 978-03877-971-44. ISBN-13: 978-0-8018-8375-0. Guesstimation: Solving the World’s Mathematical Omnibus: Thirty Einstein’s Mistakes: The Human Fail- Problems on the Back of a Cocktail Lectures on Classic Mathematics, by ings of Genius, by Hans C. Ohanian. Napkin, by Lawrence Weinstein and Dmitry Fuchs and Serge Tabachnikov. W. W. Norton, September 2008. ISBN- John A. Adam. Princeton University AMS, October 2007. ISBN-13: 978- 13: 978-0393062939. Press, April 2008. ISBN-13: 978-0-6911- 08218-431-61. (Reviewed December *Emmy Noether: The Mother of 2949-5. 2008). Modern Algebra, by M. B. W. Tent. Hexaflexagons, Probability Para- The Mathematician’s Brain, by A K Peters, October 2008. ISBN-13: 978- doxes, and the Tower of Hanoi: Martin David Ruelle. Princeton University 15688-143-08. Gardner’s First Book of Mathematical Press, July 2007. ISBN-13 978-0- Euclidean and Non-Euclidean Puzzles and Games, by Martin Gardner. 691-12982-2. (Reviewed November Geometries: Development and History, Cambridge University Press, September 2008.) fourth revised and expanded edition, 2008. ISBN-13: 978-0-521-73525-4. *Mathematics and the Aesthetic: by Marvin Jay Greenberg. W. H. Free- How Round Is Your Circle, by John New Approaches to an Ancient Af- man, September 2007. ISBN-13: 978- Bryant and Chris Sangwin. Princeton finity, edited by Nathalie Sinclair, 0-7167-9948-1. University Press, January 2008. ISBN- David Pimm, and William Higginson. *Euler’s Gem: The Polyhedron For- 13: 978-0-6911-3118-4. Springer, November 2006. ISBN-13: mula and the Birth of Topology, by Impossible?: Surprising Solutions to 978-03873-052-64. (Reviewed in this David S. Richeson. Princeton Univer- Counterintuitive Conundrums, by Julian issue.) sity Press, September 2008. ISBN-13: Havil. Princeton University Press, April Mathematics and Democracy: De- 97-80691-1267-77. 2008. ISBN-13: 978-0-6911-3131-3. signing Better Voting and Fair-Division

February 2009 Notices of the AMS 279 Reference and Book List

Procedures, by Steven J. Brams. Princ- The Presidential Election Game, by Smart, by Ian Ayres. Bantam, August eton University Press, December Steven J. Brams. A K Peters, December 2007. ISBN-13: 978-0-5538-0540-6. 2007. ISBN-13: 978-0691-1332-01. 2007. ISBN-13: 978-1-5688-1348-6. The Symmetries of Things, by Mathematics at Berkeley: A History, The Princeton Companion of Math- John H. Conway, Heidi Burgiel, and by Calvin C. Moore. A K Peters, Febru- ematics, edited by Timothy Gowers Chaim Goodman-Strauss. A K Peters, ary 2007. ISBN-13: 978-1-5688-1302- (June Barrow-Green and Imre Leader, May 2008. ISBN-13: 978-1-5688-1220-5. 8. (Reviewed November 2008.) associate editors). Princeton University Symmetry: A Journey into the Pat- Mathematics in Ancient Iraq: A Press, November 2008. ISBN-13: 978- terns of Nature, by Marcus du Sautoy. Social History, by Eleanor Robson. 06911-188-02. Harper, March 2008. ISBN-13: 978-0- Princeton University Press, August Professor Stewart’s Cabinet of 2008. ISBN13: 978-06910-918-22. Mathematical Curiosities, by Ian Stew- 0607-8940-4. The Mathematics of Egypt, Meso- art. Basic Books, December 2008. Symmetry: The Ordering Princi- potamia, China, India, and Islam: A ISBN-13: 978-0-465-01302-9. ple (Wooden Books), by David Wade. Sourcebook, by Victor J. Katz et al. Pursuit of Genius: Flexner, Einstein, Walker and Company, October 2006. Princeton University Press, July 2007. and the Early Faculty at the Institute ISBN-13: 978-08027-153-88. ISBN-13: 978-0-6911-2745-3. for Advanced Study, by Steve Bat- Tools of American Math Teaching, Measuring the World, by Daniel terson. A K Peters, June 2006. ISBN 1800–2000, by Peggy Aldrich Kidwell, Kehlmann. Pantheon, November 2006. 1-56881-259-0. (Reviewed August Amy Ackerberg-Hastings, and David ISBN 0-375-42446-6. (Reviewed June/ 2008.) Lindsay Roberts. Johns Hopkins Uni- July 2008.) Pythagorean Crimes, by Tefcros versity Press, July 2008. ISBN-13: 978- More Mathematical Astronomy Michalides. Parmenides Publishing, 0801888144. Morsels, by Jean Meeus. Willmann- September 2008. ISBN-13: 978-19309- The Unfinished Game: Pascal, Fer- Bell, 2002. ISBN 0-943396743. 722-78. (Reviewed January 2009.) mat, and the Seventeenth-Century Let- More Sex Is Safer Sex: The Uncon- Random Curves: Journeys of a ventional Wisdom of Economics, by Mathematician, by Neal Koblitz. ter That Made the World Modern, by Steven E. Landsburg. Free Press, April Springer, December 2007. ISBN-13: Keith Devlin. Basic Books, September 2007. ISBN-13: 978-1-416-53221-7. 978-3-5407-4077-3. 2008. ISBN-13: 978-0-4650-0910-7. (Reviewed June/July 2008.) Reminiscences of a Statistician: The *The Unimaginable Mathematics of *Number and Numbers, by Alain Company I Kept, by Erich Lehmann. Borges’ Library of Babel, by William Badiou. Polity, June 2008. ISBN-13: Springer, November 2007. ISBN-13: Goldbloom Bloch. Oxford University 978-07456-387-82. 978-0-387-71596-4. Press, August 2008. ISBN-13: 978- Number Story: From Counting to Roots to Research: A Vertical De- Cryptography, by Peter M. Higgins. 01953-345-79. velopment of Mathematical Problems, Springer, February 2008. ISBN-13: Unknown Quantity: A Real and by Judith D. Sally and Paul J. Sally Jr. 978-1-8480-0000-1. Imaginary History of Algebra, by John AMS, November 2007. ISBN-13: 978- *The Numerati, by Stephen Baker. Derbyshire. Joseph Henry Press, May 08218-440-38. (Reviewed December Houghton Mifflin, August 2008. ISBN- 2006. ISBN 0-309-09657-X. (Reviewed 2008.) 13: 978-06187-846-08. May 2008.) Sacred Mathematics: Japanese Tem- One to Nine: The Inner Life of Useless Arithmetic: Why Environ- ple Geometry, by Fukagawa Hidetoshi Numbers, by Andrew Hodges. W. W. mental Scientists Can’t Predict the Norton, May 2008. ISBN-13: 978- and Tony Rothman. Princeton Univer- Future, by Orrin Pilkey and Linda 03930-664-18. sity Press, July 2008. ISBN-13: 978-0- Pilkey-Jarvis. Columbia University Origami, Eleusis, and the Soma 6911-2745-3. Cube: Martin Gardner’s Mathematical *The Shape of Content: An Anthol- Press, February 2007. ISBN 0-231- Diversions, by Martin Gardner. Cam- ogy of Creative Writing in Mathemat- 13212-3. (Reviewed April 2008.) bridge University Press, September ics and Science, edited by Chandler The Volterra Chronicles: The Life 2008. ISBN-13: 978-0-521-73524-7. Davis, Marjorie Wikler Senechal, and and Times of an Extraordinary Mathe- A Passion for Discovery, by Peter Jan Zwicky. A K Peters, November matician, by Judith R. Goodstein. AMS, Freund. World Scientific, August 2008. ISBN-13: 978-15688-144-45. February 2007. ISBN-13: 978-0-8218- 2007. ISBN-13: 978-9-8127-7214-5. *Souvenirs sur Sofia Kovalevskaya 3969-0. (Reviewed March 2008.) (French), by Michèle Audin. Calvage Perfect Figures: The Lore of Num- The Wraparound Universe, by Jean- et Mounet, October 2008. ISBN-13: bers and How We Learned to Count, by Pierre Luminet. A K Peters, March Bunny Crumpacker. Thomas Dunne 978-29163-520-53. 2008. ISBN 978-15688-130-97. (Re- Books, August 2007. ISBN-13: 978-0- *Strange Attractors: Poems of Love viewed December 2008.) 3123-6005-4. and Mathematics, edited by Sarah *Plato’s Ghost: The Modernist Glaz and JoAnne Growney. A K Pe- Zeno’s Paradox: Unraveling the Transformation of Mathematics, by ters, November 2008. ISBN-13: 978- Ancient Mystery behind the Science Jeremy Gray. Princeton University 15688-134-17. of Space and Time, by Joseph Mazur. Press, September 2008. ISBN-13: 978- Super Crunchers: Why Thinking- Plume, March 2008 (reprint edition). 06911-361-03. by-Numbers Is the New Way to Be ISBN-13: 978-0-4522-8917-8.

280 Notices of the AMS Volume 56, Number 2 Doctoral Degrees Conferred 2007–2008

ALABAMA Xu, Ming, Optimal consumption rate University of Arizona (8) under certain spending behavior Auburn University (3) Department of Mathematics Department of Information Systems Department of Mathematics and Statistics and Management Science Berger, Lisa, Ranks of Abelian varieties in Statistics towers of function fields Natarajarathinam, Malini,Basestock Fernandes, Anthony, A partnership be- Ford, Robert, Path curvatures on a convex policies for the stochastic inbound roof tween a middle school teacher and a inventory routing problem novice mathematics educator centered Hollingsworth, Blane, Stochastic differ- Upreti, Rahul, Inventory policies for con- around the content ential equations: A dynamical systems tainers with stochastic returns approach Ivkovic, Milos, Characterization and cod- Wang, Huaping, Missing data analy- Moore, Emilia, On the existence of even ing techniques for long-haul optical sis in structural equation modeling— telecommunication systems and K-divisible matchings expectation maximization and multiple imputation methods McLeman, Cameron, A Gold-Shafarevich University of Alabama at equality and p-tower groups Birmingham (3) Miller, Justin,Onp-adic continued fractions and quadratic irrationals Department of Mathematics ARIZONA Baker, Steven Jeffrey, Spectral properties Arizona State Program in Applied Mathematics of displacement models University (10) Arpin, Sheree, Using mathematical mod- Goswick, Lee, Dynamical, geometric and els to investigate phenotypic oscilla- arithmetic properties of Euclidean lat- Department of Mathematics and tions in cichlid fish: A case of frequency- tices Statistics dependent selection Hamza, Eman, Localization properties Cates, Dennis, Edge detection using for the unitary Anderson model Shen, Fangfang, Approximating ideal- Fourier data with applications observer performance using Fisher University of Dur-e-ahmad, Muhammad, Structural information and the extreme value dis- plasticity of dentritic spines: A compu- tribution in detection tasks Alabama-Huntsville (3) tational study Shkarayev, Maxim, Effects of nonlinearity Department of Mathematical Erdem, Mustafa, Epidemics in structured and disorder in communication systems Sciences population with isolation and cross- immunity Duehring, Dawn, Periodic traveling wave Gehrig, Eric, Hopf algebras, projections, solutions for diffusion equations with ARKANSAS and coordinates of the first kind in time-delayed and non-local responding control theory reaction University of Arkansas at Malik, Tufail, Microbial quiescence, a sur- Hester, Anthony, Semigroups generated Fayetteville (3) by pseudo-contractive mappings under vival strategy in environmental stress the Nagumo conditions Mendez, Guillermo, Tree-based methods Department of Mathematical Sinko, Anne, Generalized colorings in to model dependent data Sciences graphs Sealey, Vicki, Calculus students’ assimilation of the Riemann integral into a Gyurov, Boyko, Maximal inverse semi- University of previously established limit structure groups of transformations Alabama-Tuscaloosa (6) Sutton, Karyn, Theoretical studies on Haller, Erin, Comparison principles for pneumococcal vaccination fully non-linear parabolic equations in Department of Mathematics Thalhauser, Craig, The two-state model Carnot groups with applications to the Raridan, Chris, Useful results for the of cancer growth: Evolutionary implica- horizontal Gauss curvature flow study of magical and expander graphs tions at the local and global scales Taylor, Phillip, Analytic bounded point Thomas, Shawanda, An optimal hedging Zhong, Zimin, Curve registration in func- evaluations and polynomial approxima- strategy for multiple commodities tional data analysis tion in the mean on crescents

The above list contains the names and thesis titles of recipients of in parentheses following the name of the university is the number of doctoral degrees in the mathematical sciences (July 1, 2007, to June 30, degrees listed for that university. A supplementary list containing names 2008) reported in the 2008 Annual Survey of the Mathematical Sciences received since compilation of this list will appear in a summer 2009 issue by 213 departments in 154 universities in the United States. Each entry of the Notices. contains the name of the recipient and the thesis title. The number

FEBRUARY 2009 NOTICES OF THE AMS 281 Doctoral Degrees Conferred

CALIFORNIA Alper, Jarod, Good moduli spaces for Group in Biostatistics Artin stacks California Institute of Bembom, Oliver, Statistical methods for Buyukboduk, Kazim, Kolyvagin systems causal inference when the assumption Technology (13) over an Iwasawa algebra of experimental treatment assignment Department of Applied and Chang, Huai-Lian, Donaldson Thomas is violated invariant of P 1 scroll Computational Mathematics Duque, David Fernandez,Resultsindy- University of California, Donaldson, Roger, Discrete geometric namic topological logic (21) homogenisation and inverse homogeni- Eichmair, Michael, Non-variational exis- Davis sation tence problems in general relativity Department of Mathematics Helgason, Hannes, Nonparametric detec- Groft, Chad Lawrence, Isoperimetric in- tion and estimation of highly oscillatory equalities on the universal covers of Breslin, William, Curvatures of surfaces signals compact spaces in hyperbolic 3-manifolds Hoch, David, Nonreflecting boundary He, Jian, Symplectic field theory of Farrell, Brendan, Analysis of noncommu- conditions obtained from equivalent subcritical Stein manifolds tative operator classes in information sources for time-dependent scattering Helleloid, Geir Trygve,Automorphism theory and harmonic analysis problems groups of finite p-groups: Structure Guan, Raymond, Advanced equalization Monro, John, Jr., A super-algebraically and applications techniques for wireless communica- convergent windowing-based approach Ramras, Daniel Alexander,Stablerep- tions to the evaluation of scattering from resentation theory of infinite discrete Hodge, Andrew, The degrees of the periodic rough surfaces groups logarithmic extension of the cotangent Sweatlock, Sarah, Asymptotic weight Wu, Baosen, Degeneration formula of bundle to the moduli of pointed curves analysis of low-density parity check Donaldson-Thomas invariants and Hitchin systems, spectral curves (LDPC) codes and KP equations Department of Statistics Tian, Lixiu, Effective behavior of dielectric Lai, (Yuan-Juang) Yvonne, An effec- elastomer composites Chang, George, Tools for multivariate tive compactness theorem for Coxeter Wang, Ke, A subdivision approach to bump hunting groups the construction of smooth differential Chen, Jiehua, Regression models with Lee, Jaejeong, Fundamental domains of forms spatially correlated errors: Applications convex projective structures Control and Dynamical Systems to urban core growth in China Liu, Shuang, Improving the classification Chen, Zehao, Estimation of high dimen- Flores, Melvin, Real-time trajectory gener- of microarray data: Supervised and sion covariance matrix and adaptive ation for constrained nonlinear dynam- unsupervised methods portfolio selection ical systems using nonuniform rational Rutherford, Daniel, Relationship between B-spline basis functions Eckner, Andreas, Two essays on credit Legendrian knot invariants default correlation Grubits, Katalin, Low-dimensional repre- Suh, Chan-Ho, Modified normal surface Horel, Guillaume, Estimating integrated sentations of transitions in molecular theories systems volatility with Markov chains Li, Ping, Stable random projections and Williams, Michael, Lens space surgeries Waydo, Stephen, Explicit object represen- on tunnel number one knots tation by sparse neural codes conditional random sampling, two sampling techniques for modern massive Wilmarth, Constance, Projections of sin- Department of Mathematics datasets gular vectors of Verma modules over Levaillant, Claire, Irreducibility of the Salzman, Julia,Spectralanalysiswith rank 2 Kac-Moody Lie algebras Lawrence-Kramer representation of the Markov chains Wright, Roy, Spatial and temporal hetero- BMW algebra of type An-1 Turnbull, Brit, Empirical null distribu- geneity of host-parasitoid interactions Tsankov, Todor, Amenability, countable tions and local false discovery rates in lupine habitat equivalence, relations and their full Ward, Gillian, Statistics in ecological Yan, Pengchong,Broadbanddetection groups modeling; the presence-only problem and imaging of multiple targets in Venzke, Rupert, Braid forcing, hyper- and other procedures clutter bolic geometry and pseudo-Anosov Zhen, Wei, Greedy functional learning Department of Statistics sequences of low entropy machine in finance Gu, Zhonghua, Model diagnostics for Claremont Graduate University of California, generalized linear mixed models University (3) Berkeley (6) Liu, Wei, Statistical network comparison School of Mathematical Sciences Department of Statistics Lu, Ruixiao, Statistical issues in detection Beasley, Joseph, Performance feedback Bhamidi, Shankar,Randomnetworks: of biological signals in the analysis of and control of solar concentrators using Flows and asymptotics microarray gene expression data wave front sensing techniques Dong, Rui, Coagulation-fragmentation Nguyen, Thuan, New procedures of fence Paolini, Christopher, A service-oriented duality for Poisson-Dirichlet distri- methods and their applications architecture for thermochemical com- butions, and exchangeable partitions Tang, En-Tzu, On estimation of the mean putation derived from Markovian coalescents squared error in small area estimation Xu, Dong, FEMVib, an ab initio multi- Peled, Ron, Global irregularities for Pois- and related topics dimensional solver for probing vibra- son processes—gravitational allocation Tseng, Szu-Ching,Ageneralizedself- tional dynamics in polyatomic molecules and rough isometries consistency approach to semiparamet- and free radicals Rocha, Guilherme, Sparsity and model ric survival models selection through convex penalties: Zhang, Zhen, Functional data analysis for Stanford University (21) Structured selection, covariance selec- densities Department of Mathematics tion and some theory Zhu, Li, Modeling dynamics in two sta- Akat, Muzaffer, A unified credit risk Traskin, Mikhail, On the consistency of tistical problems: Longitudinal disease model ensemble classification algorithms activity score and parasite infection

282 NOTICES OF THE AMS VOLUME 56, NUMBER 2 Doctoral Degrees Conferred

University of California, University of California, Taddy, Matthew,Bayesiannonparamet- Irvine (5) Riverside (5) ric analysis of conditional distributions and inference for Poisson point pro- Department of Mathematics Department of Statistics cesses Li, Xiangrong, Nonlinear simulations of Lesch, Scott, A new class of goodness-of-it University of Southern solid tumor growth using a mixture tests based on linear functions of order model: Invasion and branching statistics for the exponential distribu- California (7) tion under general Type II censoring Department of Mathematics Munteanu, Ovidiu, The structure of com- schemes plete manifolds with positive spectrum Liu, Junmei, Estimating the number of Akopian, Vardan,ModelingofEarth’s Vargas, Benjamin, Mixed end conditions species from a censored sample ionosphere and variational approach and morphogen gradient formation Wilson, Jason, On the probability of for data assimilation Webster, Micah, Nonlinear stability analy- correct selection when k is large Alaghband, Mohamad, Stochastic models sis of a free boundary problem Zhang, Qi, Different statistical tests to for understanding and pattern recogni- Wong, Chiu Fai, Zeta functions of pro- assess the validity of one-part software tion of molecular data jective toric hypersurfaces over finite reliability models DiMuro, Joseph,Onprimepowerele- fields Zhang, Wei, Logistic regression with ments of GLd(q) acting irreducibly on unknown sizes large subspaces University of California, Han, Yong Ho, Commuting triples of Los Angeles (17) University of California, matrices San Diego (12) Hiatt, Christopher, Quantum traces in Department of Mathematics Department of Mathematics quantum Teichmuller¨ space Brandman, Jeremy, A level set method Mayberry, John, The effects of noise on Angle, Robert, Holomorphic Segre pre- for calculating eigenvalues of elliptic bifurcations in circle maps with appli- serving maps operators on closed surfaces and a cations to integrate-and-fire models in proof of blow up of L∞ weak solutions Bucicovschi, Orest, Simple Lie algebras, neural biology of an aggregation equation algebraic prolongations and contract Villalobos, Jose,MonteCarlomethodsfor structures Busch, Joseph, Lower bounds in arith- FBSDEs in high dimensions metic complexity via asymmetric em- Butler, Steven, Eigenvalues and structures beddings of graphs Clark, David, Functorality for the su(3) COLORADO Epstein, Inessa, Some results on orbit Khovanov homology inequivalent actions of non-amenable Colorado State groups Guo, Hong Xin, The 3-dimensional steady gradient Ricci soliton University (13) Hinde, Colin, The essence of Ricci curva- Horn, Larissa, Fun with tensor products ture Department of Mathematics Liese, Jeffrey, Counting patterns in per- Kwon, Soonsik, Low regularity problem mutations and words Al-Azemi, Abdullah, Classification algo- of the higher order KdV type equations rithms for graphs, digraphs, and linear Nordgren, Karl, Well-posedness for the and the orbital stability issues of soliton spaces equations of motion of an inviscid, solutions incompressible, self gravitating fluid Davis, Diane,TowardatypeBn geometric Landa, Yanina, Visibility of point clouds with free boundary Littlewood-Richardson rule and exploratory path planning in un- Regev, Alon, Filtered algebraic algebras Fatemeh, Emdad, Signal fraction analy- known environments sis for subspace processing of high Richardson, Ross, Combinatorial and ge- dimensional data Leo, John, Fourier coefficients of triangle ometric problems on point processes functions Jen-Mei, Chang, Classifications on the Riehl, Amanda, Ribbon Schur functions Grassmannians: Theory and applica- Ni, Kang-Yu, Variational PDE-based im- and permutation patterns tions age segmentation and inpainting with Robinson, Daniel, Primal-dual methods applications in computer graphics for nonlinear optimization Mertens, Keith, Mathematical methods O’Donnol, Danielle, Intrinsically n-linked for fluid-solid interfaces: Meandering spatial graphs University of California, streams and sand ripples Murphy, Ethan, 2-D D-bar conductivity re- Prescott, Timothy, Invariance principles Santa Barbara (4) for random environments and shape constructions on non-circular domains Department of Statistics and Applied theorems Muskat, Jeremy, Algebraic curves over Probability finite fields Roy, Tristan,Globalexistenceofthe defocusing cubic wave equation in Bagasheva, Biliana, Bayesian methods in Peters, Pamela, Gaussian maps for double dimension 3 the investment management process covers of smooth toric surfaces Sinapova, Dima, A model for a very good Kaneda, Naohisa, Fitting mixture models Wildey, Timothy, A posteriori analysis scale and bad scale from kernel estimators of operator decomposition on interface problems Smith, S. Alex, Layered percolation on the Vestal, Douglas, Interacting particle sys- Yue, Qiao, Radial basis functions (RBFs) complete graph tems for pricing credit derivatives Wang, Dezhong, Pricing tranches of a for solving color conversion problems Souldatos, Ioannis, Characterizable cardi- CDO and CDX index nals and local Hanf numbers Department of Statistics Waelder, Robert, Elliptic genera in alge- University of California, Cao, Xiaofan, Model selection based on braic geometry Santa Cruz (2) expected square Hellinger distance Yanovsky, Igor, Unbiased nonlinear image Higgs, Megan, Clipped latent-variable Department of Applied Mathematics registration spatial models for ordered categorical and Statistics Zhu, Mingqiang, Fast numerical algo- data rithms for total variation based image Patil, Anand, Bayesian nonparametrics Wu, Rongning, Estimation for some linear restoration for inference of ecological dynamics and nonlinear time series models

FEBRUARY 2009 NOTICES OF THE AMS 283 Doctoral Degrees Conferred

University of Colorado, Moulton, Derek,Mathematicalmodeling FLORIDA of field driven curvature surfaces Boulder (9) Florida Atlantic Department of Mathematics Ronkese, Robert, The analysis and numerical simulation of a mathematical University (1) Bruns, Corey, Variations of independence model of bone growth and reabsorption Department of Mathematical in Boolean algebras Vasquez, Paula, Modeling wormlike mi- Sciences Davenport, John,AnalysisofAmerican cellar solutions options Kalis, Jan, Sobolev inequalities Zhang, Ningyi, Inverse problem for wave Ernst, Dana, A diagrammatic represen- propagation in a perturbed layered tation of an affine C Temperly–Lieb Florida Institute of half-space and orthogonality relations algebra in poroelastic materials Technology (4) Formichella, Marc, Functional equations Department of Mathematical among Barnes’ integrals and hypergeo- Zhang, Xinyi, Expected length of mini- metric series mum spanning tree Sciences Mann, Allen, Independence-friendly cylin- Mamillapalle, Sameer, A study of func- dric set algebras tional differential equations with antic- Nickodemus, Matthew, Natural dualities DISTRICT OF ipation and retardation for finite groups with Abelian Sylow Sartor, Kenneth, A study of variational subgroups COLUMBIA phase estimation methods for synthetic Pohlmann, Brent, Structural properties aperture radar applications of acyclic heaps with applications to George Washington Seetharaman, Hariharan, Adapted wave- Kazhdan-Lusztig theory University (9) let methods for heat equation on un- Radhakrishnan, Vinod, An asymptotic bounded domains formula for the number of non-Serre Department of Mathematics Shaykhian, Gholam,Integrationandop- curves in a two parameter family of timization: Irrational numbers for ran- elliptic curves Andress, Tanya, The spectrum and the dom sequences and scope of evolution- ˇ Seguin, Troy,Riskmeasures first Cech cohomology group of a one ary algorithms dimensional tiling dynamical system CONNECTICUT Barg, Michael, Direct methods in the Florida State calculus of variations with applica- University (15) University of Connecticut, tions to tendon-reinforced piecewise- isotropic membranes Department of Mathematics Storrs (9) Jasso-Hernandez, Fanny,Ahomological Chan, Wan-Kan, Analysis and approxima- Department of Mathematics algebraic approach to the Tutte polyno- tion of a two-banded Ginzburg-Landau Bowers, Adam, The Grothendieck in- mial model of superconductivity equality: Methods and applications McKenna, Geoffrey, Graphs, algebra, and Chen, Zheng, ANOVA for parameter de- Kaur, Sawinder Pal, An eigenvalue prob- probability pendent nonlinear PDEs and numerical methods for the stochastic Stokes equa- lem for some nonlinear transformation Niebrzydowski, Maciej, Some applications of multidimensional arrays tions of quandles and their homology to the Culham, Andrew, Asset pricing in a Lu- Ranasinghe, Sudath, Model to develop a geometry of knots provision for adverse deviation (PAD) cas framework with boundedly rational heterogeneous agents for the mortality risk of impaired lives Department of Statistics Moreno, Juan, Impulse control problems Department of Statistics Davi, Ruthanna, Joint testing of sensitiv- under non-constant volatility Das, Sourish, Generalized linear models ity, specificity, and kappa in diagnostic Nguyen, Hoa, Centroidal Voronoi tes- and beyond: An innovative approach studies selations for mesh generation: From uniform to anisotropic adaptive trian- from Bayesian perspective Huang, Dalong, Effects of contamination gulations Guo, Feng, Modeling genetic data using on statistical inference using sib-pair Bayesian hierarchical models analysis Novocin, Andrew, Factoring univariate Li, Pengfei, A factor and vector-AR model polynomials over the rationals Shu, Yu, Group sequential designs and for analyzing high dimension volatility Saka, Yuki,AnalysisoftwoPDEmodels inference of a medical diagnostic test for high frequency financial data in fluid mechanics: Nonlinear spectral with binary outcomes Mukhopadhyay, Jaydip, Mining tools for eddy-viscosity model of turbulence and high-dimensional time series data using VanRaden, Mark, Cumulative logit-Poisson infinite-Prandtl-number model of man- spectral methods and cumulative-logit negative binomial tle convection Xi, Yingmei, New development of Bayesian compound regression models for count Singleton, Lee, Geometric and computa- mixture models for survival and survey data tional generation, correction, and sim- data plification of cortical surfaces of the Yu, Fang, Bayesian methods for high- Howard University (3) human brain throughput gene expression data in Zhu, Wuming, A spectral element method Department of Mathematics bioinformatics to price European options Attimu, Dodzi, Linear operators on some Department of Statistics DELAWARE non-Archimedean Hilbert spaces and their spectral theory Choi, Seo-eun, A statistical approach to ocean circulation inverse problem University of Delaware (6) Dembele, Bassidy, Malaria model in peri- He, Jianghua, Time-varying coefficients Department of Mathematical Science odic environments models for longitudinal aging data Beckham, Jon Regan, Analysis of mathe- Legette, Lakeshia, Maximal groups in Norton, Jon, Spatiotemporal Bayesian matical models of electrostatically de- the Stone-Cechˇ compactification of a hierarchical models, with application formed elastic bodies discrete semigroup to birth outcomes

284 NOTICES OF THE AMS VOLUME 56, NUMBER 2 Doctoral Degrees Conferred

Stefanov, Dimitre, Cardiovascular risk Naranjo, Arlene, State-space models with Department of Mathematics and functions based on multi-state models exogenous variables and missing data Computer Science Tan, Fei, A method for finding the nadir Papageorgiou, Georgious,Multivariate Hanson, Lauren, Techniques in con- of non-monotonic relationships limited translation estimators strained optimization involving partial Uhm, Dai Ho, Flexible additive risk mod- Roy, Ananya, Empirical and hierarchical differential equations els using piecewise constant hazard Bayesian methods with applications to functions Magnant, Colton, Partitions of graphs small area estimation under distance constraints University of Central Ryu, Euijung, Modeling and inference for Nastase, Esmeralda, Color criticality and an ordinal effect size measure chromatic connectivity of graphs Florida (4) Saha, Sourish, Response surface designs Department of Mathematics for linear mixed models Georgia Institute of Flores, Paul, Categorical properties of Santra, Upasana, Probability matching Technology (7) lattice-valued convergence spaces priors for the bivariate normal distribution School of Mathematics Holmquist, Sonia, An examination of the effectiveness of the Adomian de- Carroll, Christina, Enumerative combina- composition method in fluid dynamic University of South torics of posets applications Florida (12) Inkmann, Torsten, Tree-based decom- Vogel, Thomas, Soliton solutions of non- Department of Mathematics positions of graphs on surfaces and linear partial differential equations applications to the traveling salesman using variational approximations and Adhikari, Dhruba R., Applications of problem inverse scattering techniques degree theories to non-linear operator Kampel, Guido,Mathematicalmodeling Wlodarczyk, Tomasz, Stability and preser- equations in Banach spaces of fines migration and clogging in vation properties of multisymplectic Andreevska, Irena,Mathematicalmod- porous media integrators eling and analysis of options with Kettner, Michael, Algorithmic and topo- jump-diffusion volatility logical aspects of semi-algebraic sets (21) University of Florida Daqqa, Ibtisam, Subconstituent algebras defined by quadratic polynomials Department of Mathematics of Latin squares Lessard, Jean-Philippe, Validated continu- Aslan, Beyza, A continuous approach to Davis, John C., Identification of parame- ation for infinite dimensional problems the lightning discharge ters when the density of the minimum Ulusoy, Suleyman, The mathematical the- Brodhead, Paul, Computable aspects of is given ory of thin film evolution closed sets Genova, Daniela, Forbidding and enforc- Viveros-Rogel, Jorge, An extension of Chen, Pengwen,Bergmanmetricsand ing of formal languages, graphs, and KAM theory to quasi-periodic breather their applications partially ordered sets solutions in Hamiltonian lattice system Coleman, Micah, Asymptotic enumera- George, Florence, Johnson’s system of tion in pattern avoidance and in the distributions and microarray data anal- University of Georgia (13) ysis theory of set partitions and asymptotic Department of Mathematics uniformity Hoare, Armando, Parametric, non-para- Nguyen, Hung Ngoc, Representations of metric and statistical modeling of stony Cinkir, Zubeyir,Thetauconstantof finite groups of Lie type coral reef data metrized graphs Sabuwala, Adnan, A convergence study Ibrahimu, Boubakari, The Leray-Schauder Cooper, Bobbe Jane, Support varieties for of spectrally matched grids in the approach for the topological degree of tilting modules for GLn presence of non-smooth data and perturbed maximal monotone opera- Davie, Emille Kennae, Characterizing anisotropy tors right-veering homeomorphisms of the Strich, Robert, Passive states and es- Mbah, Alfred K., On the theory of records punctured torus via the Burau repre- sential observers in algebraic quantum and applications sentation of B3 field theory Shih, Shou Hsing, Forecasting models for Liu, Haipeng, Prewavelet solution to Venkataraman, Prabhu,The2-lienofa economic and environmental data Poisson equations 2-gerbe Staninska, Ana, A theoretical model for Petrov, Peter Konstantinov,Nashproblem Zeng, Qingguo, Diffusion weighted mag- flexible tiles self-assembly on spaces of arcs netic resonance image analysis and Taylor, Rodney, Lagrange interpolation Platt, Kenyon, Classifying the represen- medical image registration on Leja points tation type of infinitesimal blocks of Zheng, Xiqiang, Efficient Fourier trans- category OS forms on hexagonal arrays Rusinko, Joseph Patrick, Equivalence of Department of Statistics GEORGIA mirror families constructed by toric degenerations of flag varieties Baldwin, Jamie, Evaluating adjustments (6) Wright, Caroline, Second cohomology to the mean squared error due to es- Emory University groups of Frobenius kernels timating variance parameters in linear Department of Biostatistics mixed models Wu, Jianbao,SphericalsplinesforHer- Giurcanu, Mihai, Biased bootstrap for Chen, Huichao, Statistical methods for mite interpolation and surface design semiparametric models modeling exposure and reproductive outcomes Department of Statistics Lee, Keunbaik, Marginalized regression models for longitudinal categorical data Crawford, Sara, Multiple sources of in- Cai, YiMei, Estimation of the seed disper- formative dropout in longitudinal data Li, Hongying, Mapping quantitative trait sal distribution with genotypic data nucleotides with longitudinal data sub- Wannemuehler, Kathleen, Likelihood- Iaci, Ross, Multivariate association and ject to non-ignorable dropout based measurement error adjustments dimension reduction Liu, Tian, Bayesian functional mapping in occupational and environmental ex- Park, Jin-Hong, Dimension reduction in of complex dynamic traits posure studies time series

FEBRUARY 2009 NOTICES OF THE AMS 285 Doctoral Degrees Conferred

Zhang, ChenHua, Applications of smoothly Department of Statistics Ke, Baoguan, A method for genetic varying functions and tail index estima- mapping of quantitative traits and Ge, Yang, Bayesian inference with mix- tion related statistical problems tures of logistic regression: Functional approximation, statistical consistency Kim, Su Yeon, Adaptive evolution of ILLINOIS and algorithmic convergence conserved non-coding elements Rhoads, Christopher, Utilizing prior in- Lim, Chae Young, Characteristics of a formation about the variance structure model error in an air quality model and Illinois Institute of fixed-domain asymptotic properties of Technology (2) Southern Illinois spatial cross-periodograms Zhao, Zhibiao, Nonparametric inference (3) Department of Applied Mathematics University, Carbondale for stochastic diffusion models Department of Mathematics Erickson, John F., Generalized native University of Illinois at spaces Abuhassan, Hassan, Some transformed Ortega, Oscar, Consensus and location: distributions Chicago (18) The mean function Lin, Yuan, High-order finite difference Epidemiology and Biostatistics methods for solving heat equations Division Northern Illinois deSouza, Comlan, Periodic eigenfunc- University (4) tions of the Fourier transform operator Evans, Charlesnika, Blood stream infec- tions in veterans with spinal cord injury Department of Mathematical University of Chicago (22) Fitchett, George, The role of daily spiritual Sciences experience in cardiovascular disease Department of Mathematics Cappetta, Robert, Reflective abstraction Gao, Sasha, Information recovery from and the concept of limit: An experimen- Bremer, Christopher,AnEulerintegral surrogate outcomes in incomplete lon- tal study formula for epsilon factors of connec- gitudinal data tions Kisunzu, Phillip, Teacher instructional Mattson, Christine, Risk compensation, practices, students’ mathematical dis- Csima, Nora Elizabeth,Newton-Hodge circumcision, and HIV prevention in positions and mathematics achieve- filtration for F-crystals with structure Kisumu, Kenya ment Day, Matthew, Symplectic structures on McIntyre, Anne, Lessons learned from Poliak, Cathy, Observed confidence levels right-angled Artin groups: Between the surveillance for bacterial infectious dis- for regression parameters mapping class group and the symplectic eases group Santra, Sourav, Some contributions to Qualls-Hampton, Raquel, Health-related ¨ design and analysis of crossover exper- Gashi, Qendrim, A conjecture of Kottwitz quality-of-life and pain in an SCI popu- iments and Rapoport for split groups lation: Descriptive and factor Geline, Michael, Modular representation Mathematics, Statistics & Computer theory and the Schur index Northwestern Science Department Guillou, Bertrand, On some properties of University (11) motivic cohomology Cashen, Christopher, Quasi-isometries Department of Mathematics Kamgarpour, Masoud, Stacky Abelianiza- among tubular groups tion of connected algebraic groups Chan, Kungho, Local positivity and Alexander, Gary Clark, Index theo- Seshadri constants rems on noncommutative two-tori and Lange, Karen, The computational com- Hochschild cohomology of quantum plexity of homogeneous models Fathallah-Shaykh, Hassan,Modelingand special linear groups Lee, Benjamin, On the algebraic de Rham local filtering of noise embedded in complex genome-scale microarray datasets Bailey, Scott, Topological splittings of spectra related to tmf Longo, Nicholas P. M., Quasilinear Schro-¨ He, Peng, The risk neutral dynamics dinger equations of market implied volatility and its Chu, Chenghao, Representing cohomol- application ogy theories in the triangulated cate- Masson, Robert, The growth exponent for gory of motives planar loop-erased random walk Krop, Elliot, Enumerating matchings in regular graphs Dhand, Vivek, Geometric Langlands dual- Nguyen, Tu Ahn, Unique continuation ity and forms of reductive groups for parabolic equations and local well- Rafalski, Shawn, Immersed turnovers in posedness for mKdV equation hyperbolic 3-orbifolds Novak, Christopher,Groupactionsvia interval exchange transformations Peng, Irine, Quasi-isometries of some Vozoris, Kathryn,Thecomplexfieldwith solvable groups a predicate for the integers Department of Engineering Sciences Schedler, Travis, Differential operators Yuce, Iker, Decompositions of 2-generator and Applied Mathematics and Batalin-Vilkovisky structures in free Kleinian groups and hyperbolic dis- noncommutative geometry placements Donovan, Graham, Rare event simula- Tikaradze, Akaki, The center and repre- Zhang, Weiya, Designs for a toxicity- tion systems using the cross-entropy sentations of infinitesimal Hecke alge- efficacy model and inference on a method bra normal mean with known coefficient of Kao, Justin, Mathematical modeling, sim- Wallace, Christopher,Galoisandmotivic variation ulation, and analysis of two problems Galois groups Zhao, Ailing, Newton’s method with de- in interfacial fluid dynamics Zbarsky, Boris, On some stratifications of flation for isolated singularities of poly- Tikhomirova, Anna,Mathematicalmod- affine Deligne-Lusztig varieties for SL3 nomial systems eling of structure formation in angio- Zhou, Ling, Association rule mining and Department of Statistics genesis quantitative association rule mining Vaughan, Benjamin, Applications of the Hugeback, Angela, Point process models among infrequent items extended finite element method in for astronomy: Quasars, coronal mass Zhuang, Yan, Parallel implementation of mathematical biology ejections and solar flares polyhedral homotopy methods

286 NOTICES OF THE AMS VOLUME 56, NUMBER 2 Doctoral Degrees Conferred

University of Illinois, INDIANA Validashti, Javid, Multiplicities of graded Urbana-Champaign (24) algebras Indiana University, Vizcarra, Andrew, Regularity of sub- Department of Mathematics Bloomington (8) Gaussian processes and other random fields Azgin, Salih, Model theory of valued Department of Mathematics difference fields Wang, Chunbo, Mixed finite element Duncan, Jonathan, First return recov- methods for the Stokes and Navier- Bansal, Shivi, Rational points on lattice ery of Baire class one functions on Stokes equations varieties ultrametric spaces Yalcin, Umud,Rankthreesymplectic Cao, Zhu, Product identities for theta Franko, Jennifer, Braid group representa- groups functions tions via the Yang Baxter equation Yang, Xiaofeng, Modeling, analysis and Chaiya, Somjate, Complex dynamics and Irwin, Trevor, Fraisse limits and colimits simulation of multi-phase flows Salem numbers with applications to continua Zhang, Pei,Mathematicalmodelingof Ferguson, Colin, Chain conditions on Jung, Min Kyung, Statistical methods for host-parasite dynamics subnormal subgroups biological applications Zhao, Yanhong, On forward-backward Forgacs, Tamas, Interpolation of weighted Pham, Du,Comparisonoffinitevol- stochastic differential equations and 2 L -holomorphic functions in higher di- ume and finite difference methods and related numerical methods mensions convergence results for finite volume Department of Statistics Hu, Yong, Localization of divisors of inte- schemes gers and of some arithmetic functions She, Chunfeng, A mathematical model Chen, Hui, Voice over the internet: Statis- Huber, Timothy, Zeros of generalized for power derivatives tical properties and quality of service Rogers-Ramanujan functions and topics Zhang, Siyu, Pricing caps and swap- Cheng, Riyan, Statistical methods for from Ramanujan’s theory of elliptic tions when bond prices follow jump- mapping multiple complex traits functions diffusion processes and have log-price Knapp, Shannon, Incorporating uncer- Kadziela, Samuel, Rigid analytic uni- volatility tainty into non-invasive DNA-based formization of hyperelliptic curves Zhou, Chunlai, Complete deductive sys- mark-recapture population estimates Kilbourn, Timothy, Congruence proper- tems for probability logics with appli- Lu, Zhenqiang, Stenosis surveillance of ties of Fourier coefficients of modular cations in Harsanyi type spaces hemodialysis patients forms Indiana University-Purdue Xu, Hui, Some applications of the prior Kou, Ming, Existence and convergence Bayes approach of stochastic Loewner evolution in University Indianapolis (1) Xu, Huiping, Estimation of a general cor- multiply connected domains Department of Mathematical relation structure for latent class and Malicki, Maciej, Topologies and metrics Sciences latent variable models of multivariate on Polish groups binary data Ramsey, Bobby, Jr., A generalization of Zhang, Jianying, Algorithm-based sta- Moreno, Javier, Iterative differential the Lyndon-Hochschild-Serre spectral tistical modeling with application to Galois theory in positive characteris- sequence for polynomial cohomology tic: A model theoretic approach multi-sensor tracking data with missing values Pahlajani, Chetan, Stochastic averaging Purdue University (26) correctors for a noisy Hamiltonian Department of Mathematics University of Notre system with discontinuous statistics Park, Seung Kook, Applications of alge- Azar, Monique, Some lower and upper Dame (5) braic curves to cryptography bounds in real algebraic geometry Department of Mathematics Blanco-Silva, Francisco, The curvelet trans- Prince, Noah, Deltz-system methods in Chailuek, Kamthorn, An extension of contemporary graph theory form. A generalized definition and approximation properties Bergman spaces and their Toeplitz Schoretsanitis, Konstantinos, Fraisse the- Deger, Mustafa Ersin, A biholomorphism operators ory for metric structures from the Bell representative domain Eleftheriou, Panteleimon, Groups defin- Sinthaveelert, Malinee, Prescribing dila- onto an annulus and kernel functions able in linear o-minimal structures tions in space Dwelle, Kayla, Some results on Hadamard Harper, John, Quillen homology of mod- Suer, Sonat, Model theory of differentially closure and variation diminishing prop- ules over operads closed fields with several commuting erties of totally nonnegative matrices Jones, Benjamin, On the singular Chern derivations Gu, Nan, Some results in the problem of classes of Schubert varieties via small Vandenbussche, Jennifer, Five topics in simultaneous resolution of singularities resolution extremal and structural graph theory Kumar, Manish, Fundamental group in Quinn, Sara, Algorithmic complexity of Wang, Chunlin, On the estimator of the positive characteristic algebraic structures density of Feynman-Kac semigroups of Lomeli, Luis, Functoriality for the classical 2-stable-like processes and the purely groups over function fields IOWA discontinuous Girsanov transform of Maxin, Daniel, The interplay of isolation 2-stable-like processes from reproduction with demography Iowa State University (11) Wu, Qingquan, Algorithmic aspects of and sexually transmitted diseases Department of Mathematics biquadratic cubic and radical function Mitchell, Ronald (Chris),Hochschildco- field homology and the Smith resolution Chung, Key One, Weak homomorphisms Xiong, Maosheng, Distribution of Selmer Siudeja, Bartlomiej, Properties of heat of coalgebras groups of quadratic twists of a family kernels Fiedler, James, Greco-Latin squares as of elliptic curves Tan, Kuan, Applications of the Schwarz bijections Department of Statistics function to a class of multiply con- Halverson, Matthew, Asymptotic behav- nected domains with symmetries ior of the solutions to a family of PDE’s Li, Di, Markov chain marginal bootstrap Tapp, Darren, Bernstein-Sato polynomi- arising from the chemotaxis equations for generalized estimating equations als and Picard-Lefschetz monodromy of Keller and Segal

FEBRUARY 2009 NOTICES OF THE AMS 287 Doctoral Degrees Conferred

Meng, Qiang, Topics in pricing American Diaz, Esteban, Connections between ho- Yasong, Jin, Maximum queue length of a type financial contracts mology group planes, and flocks of fluid model with a Gaussian input Rice, Theodore,Greedyquasigroupsand quadratic cones greedy algebras with applications to Duan, Yanzheng,Onsomegeometricand Wichita State University (1) combinatorial games approximation properties in Banach spaces Department of Mathematics and Wang, Zhongming, Development of level Statistics set method for computing the semi- Hamon, Suzanne, Some topics in t-fac- classical limit in Schrodinger¨ equations torizations Harder, Theodore, Some remarks on with potentials Llosent, Giovanna, Stable endomorphism constructive Yukawa theory in four rings and Ext groups for the symmetric dimensions Department of Statistics group S4 Chatterjee, Arindam, Applications of Ortiz-Albino, Reyes, On generalized non- asymptotic expansions to some sta- atomic factorizations KENTUCKY tistical problems Reif, Kathleen, Hyperbolicity of arbores- Huckett, Jennifer, Synthetic data methods cent tangle spaces University of Kentucky (7) for disclosure limitation Rivera, Joaquin, Existence of traveling Department of Mathematics Lawrence, Michael, Interactive graphics, wave solutions for a nonlocal reaction- diffusion equation graphical user interfaces and software Clift, Shawn, Generalized Witt vectors interfaces for the analysis of biological Stoeckel, Matthew, Computing quantum hyperbolic invariants Godefroy, Hugh,Astudyoforienta- experimental data and networks tion maps: Crystallographic symmetry, Taylor, Scott, Options pricing Ott, Ellis, Schools left behind; statistical mean orientation, and applications issues with NCLB (No Child Left Behind) Wendt, Theodore, Mixed complementarity Kiteck, Daniel, Covers of models Wickham, Hadley, Practical tools for formulations and energy balance in Petrovic, Sonja,Algebraicandcombina- exploring data and models dynamic contact problems torial properties of certain toric ideals Department of Statistics and in theory and applications University of Iowa (27) Actuarial Science Shin Kim, Aekyoung,TheLp Neumann Department of Applied Mathematics Feng, Dai,BayesianhiddenMarkovnor- problem for Laplace’s equation on con- and Computational Science mal mixture models with application to vex domains MRI tissue classification Choi, Yang Ho, Curvature arbitrage Slone, Michael, Homological combina- Gao, Xiaoli, Penalized methods for high- torics and extensions of the cd-index Kwon, Hun, W 2,p estimates for linear dimensional least absolute deviation Zhang, Wei, GMRES on a tridiagonal fourth order elliptic equations with regression BMO coefficients in Reinfenberg flat Toeplitz linear system domains Ko, Bangwon, On sums of dependent heavy-tailed random variables and val- University of Louisville (4) Medikonduri, Ram Kishore, Tabulation of uation of equity-linked insurance prod- tangles and solving tangle equations ucts Department of Mathematics Nicholson, Neil, On knots and their Lee, Yeonok, A mixture of semiparametric invariants models Nowrouzi Kashan, Fariba,Costshifting Ortiz-Rosado, Ricardo,Newton/AMGal- of the drug-eluting stent gorithm for solving complementarity Petrou, Christiana, Use of text mining to problems arising in rigid body dynam- KANSAS predict patient compliance ics with frictional impacts Kansas State University (5) Tesfamicael, Mussie, Forecasting pre- Pansera, Jerome, Local risk minimization, scription of medications and cost anal- consistent interest-rate modeling and Department of Mathematics ysis using time series applications to life insurance Adongo, Donald, A local extrapolation Wiglesworth, Lesley, A study of unit bar-visibility graphs Department of Biostatistics method for hyperbolic conservation laws: The ENO and Goodman-LeVeque Minggen, Lu, Analysis of panel count data underlying schemes and sufficient con- using monotone polynomial splines ditions for TVD LOUISIANA Shi, Qian, Bayesian methods of evaluation Chen, Weidong, An efficient method for and use of surrogate endpoints in the an ill-posed problem—band-limited ex- Louisiana State single-trial settings trapolation by regularization University, Baton Tan, Huaming, Variable selection and Department of Statistics estimation in the partially linear AFT Rouge (5) model Bsharat, Rebhi,EvaluationofnCk estima- Department of Mathematics tors Zhang, Suhong, Inference on association measure in copula model for bivariate Liu, Ying, On goodness-of-fit of logistic Daspan, Gideon,ComparisonofKPand survival data with hybrid censoring and regression model BBM-KP models application to a HIV study von Borries, George Freitas, Partition Kim, Heon, Sign ambiguities of Gaussian Zugui, Zhang, Model selection for nearly clustering of high dimensional low sums sample size data based on p-values replicated data based on conceptual Laubinger, Martin, Differential geome- predictive statistics try in Cartesian closed categories of University of Kansas (3) smooth spaces Department of Mathematics Department of Mathematics Namli, Suat, Multiplicative renormaliza- Bennett, Lucas, Edge index and arc index Parker, Kenneth, Some results in obstruction method for orthogonal polynomi- of knots and links tion theory for projective modules als Caprau, Carmen, An sl(2) tangle homol- Xiaobo, Liu, Some problems in the sto- Wallace, Steven, Surgery description of ogy and seamed cobordisms chastic portfolio theory colored knots

288 NOTICES OF THE AMS VOLUME 56, NUMBER 2 Doctoral Degrees Conferred

Louisiana Technology Li, Xianbin, Modeling composite outcome Marotta, Sebastian,Thecomplexdynam- University (4) and jointly modeling its components ics of singularly perturbed rational Lu, Yun, Detecting and contending with maps Mathematics and Statistics Program the influence of “unmeasured” con- Matsura, Ryota, Twisted root numbers Du, Xudong, A finite difference method founders of elliptic curves semistable at primes for studying thermal deformation in a Luo, Sheng, Mixed effects stochastic above 2 and 3 3D microsphere exposed to ultrashort process models of smoking cessation Mikitchenko, Oleg, Applications of the pulsed lasers behavior resolution of singularities to asymptotic Liu, Chang, Stochastic modeling of retail Manichaikul, Ani, Statistical methods for analysis of differential equations mortgage loans based on past due, mapping quantitative trait loci in ex- Wahl, Eric, Geodesics on isopotential prepaid, and default states perimental crosses surfaces and solutions to Newton’s Nilsen, Erik Alfonso, Nonlinear dynamical McGready, John, Two studies on current N-body problem analysis of brain electrical activity due issues in biostatistical education Yeats, Karen,Growthestimatesfor to exposure to weak environmentally Ning, Jing, Estimating causal treatment Dyson–Schwinger equations relevant electromagnetic fields effects for post-randomization marker Zollinger, Elizabeth, A family of comets Niu, Tianchan, A hyperbolic two-step data with failure event censoring in the three-body problem model based finite difference method Su, Shu-Chih, Structure/function rela- for studying thermal deformation tionships in the analysis of anatomical Boston University School and functional neuroimaging data of Public Health (6) Tulane University (3) Wang, Weiwei, Counterfactual inference Department of Mathematics from observational data: Methods and Department of Biostatistics applications Cho, Kelly, Handling linkage disequilib- Aranda, Vivian, Computational model- Yin, Yue, Bayesian analysis of infectious ing of peristaltic pumping using the rium in linkage analysis using dense disease time series data and optimal SNPs method of regularized Stokeslets constrained Bayesian updating Medina, Luis, Case studies of experimen- Lee, Sophia, Analysis of correlated binary Zhou, Yijie, Association of mortality rates data in non-inferiority trials tal mathematics: p-adic valuations of with race and income among U.S. Montez-Rath, Maria, Models for non- recurrences Medicare participiants Musielak, Magdalena, A computational additive interaction effects model of nutrient transport and acqui- Department of Mathematics Scaramucci, Amy,Amodifiedlogrank sition by diatom chains in a moving Baugher, Ben, Statistics of critical points test to account for left truncated sur- fluid in Kahler geometry and string theory vival data: A comparison with the usual log rank test Choi, Sung Rak, The geography of models University of Louisiana at and its applications Wang, Ling, Bayesian model-based clus- Lafayette (4) MacDonald, Brian, Statistics of non-real tering of short-time series Department of Mathematics zeros and critical points of systems Yin, Xiaoyan, Genetic association analy- of real random polynomials in several ses of time-to-event data: Selection bias Carrillo-Escobar, Julio,Blow-upand variables and imputation from the Framingham quenching phenomena for singular Wang, Shaui, On a certain triple system, Heart Study semilinear parabolic problems elliptic curves and Gauss theory of Choudhury, Jayanta, Numerical and quadratic forms Brandeis University (2) asymptotic investigation of the station- Zhong, Qi, Energies of zeros of random Department of Mathematics ary-propagated localized solutions of sections on Riemann surfaces the Boussinesq equation in two dimen- Tseng, Jimmy, On shrinking target prop- sions University of Maryland, erties Lu, Fei, ANOVA and MANOVA under Wong, Dong,SpikedmodelsinWishart (4) heteroscedasticity Baltimore County ensemble Treeyaprasert, Tawikan,Blow-upand Department of Mathematics and quenching phenomena due to a con- Statistics Harvard University (37) centrated nonlinear source on a semi- Li, Feng, Statistical inference for pro- Department of Biostatistics infinite interval teomics Aryee, Martin, Leveraging hidden corre- Siddani, Ravi, Spatio-temporal modeling lations in high-dimensional biological MARYLAND of rain rates data Soane, Ana Maria, Variational problems Basagana Flores, Xavier, Design of obser- in weighted Sobolev spaces with appli- Johns Hopkins vational longitudinal studies University (18) cations to computational fluid dynamics Ding, Xiao, Family-based association tests with longitudinal measurements Department of Biostatistics Sun, Zhibin, Geomagnetic data assim- Fardo, David, Statistical issues in genome- Achy-Brou, Aristide, Three novel ap- ilation using ensemble methods to wide association studies proaches to analyzing longitudinal data: estimate forecast error covariance Regression on longitudinal propensity Hedt, Bethany, Novel methods for effi- scores, enhanced sensitivity analysis MASSACHUSETTS cient surveillance and monitoring framework and marked renewal sto- Loerch, Patrick, Using mixed effects mod- chastic processes Boston University (7) els to integrate high-dimensional, ge- An, Ming-Wen,Ontheimportanceof nomic data and an array-based analysis Department of Mathematics and designs in better addressing missing of the evolution of brain aging data due to death and to loss-to-follow- Statistics Mar, Jessica, Stochastics and networks in up Busuioc, Cecilia, Eisenstein cohomology, genomic data Colantuoni, Elizabeth,Topicsincausal Milnor K-theory and special values of McDaniel, Samuel, The analyses of array estimation for public health research L-functions CGH data and current status data

FEBRUARY 2009 NOTICES OF THE AMS 289 Doctoral Degrees Conferred

Orellana, Liliana, Methodological chal- Michael, Loizos, Autodidactic learning Straus, Kenneth, Validation of a proba- lenges for the estimation of optimal and reasoning bilistic model of language acquisition dynamic treatment regimes from ob- Roper, Marcus,Symmetrybreakingand in children servational studies un-breaking in microhydrodynamical Pei, Lixia, Design and analysis of quantile systems: Swimming, pumping and bio- Tufts University (2) equivalence bridging trials ballistics Department of Mathematics Thorpe, Christopher, Probably correct, Ravichandran, Caitlin, Joint modeling Caterina, Gianluca,Leastactionprinci- secrecy preserving computation and its of longitudinal and state-change pro- ples and additive invariants for a class application in auctions and securities cesses of reversible cellular automata exchanges Wang, Rui, Nonparametric methods for Munro, Erin C., The axonal plexis: A Vlah, Dario, Antenna selection perfor- inference after variable selection, com- description of the behavior of a network mance in 802.11 networks parisons of survival distributions, and of axons connected by gap junctions random effects meta-analysis, and re- Yamins, Daniel, A theory of local-to- porting of subgroup analyses global algorithms for one-dimensional University of spatial multi-agent systems Department of Mathematics Massachusetts, Alvine, Amanda, Investigation of J-holo- Massachusetts Institute Amherst (8) morphic curves in M3 × S1 of Technology (17) Department of Mathematics and Anno, Irina, Weak representation of tan- Department of Mathematics Statistics gle categories in algebraic geometry Chebikin, Denis, Polytopes, generating Are, Sasanka, Coarse-graining dynamics Chen, Dawei, Covers of elliptic curves of interacting particle systems and slopes of effective divisors on the functions, and new statistics related to Beheshti, Shabnam, Solutions of dilaton moduli space of curves descents and inversions in permuta- tions field equations with applications to the Fedorchuk, Maksym, Severi varieties and soliton-black hole correspondence in the moduli space of curves Fang, Chuying, Ad-nilpotent ideals of complex and real reductive groups generalized JT gravity Freer, Cameron, Models with high Scott Damon, Eli, Analysis of the Gauss-Green rank Francis, John, Derived algebraic geometry over E -rings form on the moduli space of unduloids Harvey, David, Algorithms for p-adic n Gu, Jerin,Single-petaledK-types and Diehl, Michael, Large deviations of ob- cohomology and p-adic heights Weyl group representations for classical servables in classical and quantum Lan, Kai-Wen, Arithmetic compactifica- groups lattice spin systems tions of PEL-type Shimura varieties Havlickova, Marketa, Boundaries of K- Fenn, Molly, Generating equivalence class Pottharst, Jonathan,Selmergrowthanda types in discrete series of B-stable ideals “triangulordinary” local condition Herring, Gregory, Some applications Kamrin, Kenneth, Stochastic and deter- Smyth, David, Compact moduli of sin- ministic models for dense granular of computational mathematics: Tumor angiogenesis and Bose-Einstein conden- gular curves: A case study in genus flow sates one Konvalinka, Matjaˇz, Combinatorics of Oh, Choonghong, Well-posedness theory determinantal identities Department of Statistics of a one parameter family of coupled Lee, Peter,Grobner¨ bases in rational Fan, Xiaodan, Integrating correlated data- KdV-type systems and their invariant homotopy theory Gibbs measures sets to improve inference in computa- Lipyanskiy, Maksim, A semi-infinite cycle tional biology VonRenesse, Christine, Combinatorial as- construction of Floer homology pects of toric varieties Liu, Jingchen, Effective modeling and sci- Montarani, Silvia, Finite dimensional rep- entific computation with applications to resentations of symplectic reflection Worcester Polytechnic health study, astronomy, and queueing algebras for wreath products network Institute (1) Rubinstein, Yanir Akiva,Geometricquan- School of Engineering and Applied tization and dynamical constructions Department of Mathematical Science on the space of Kähler metrics Sciences Rycroft, Christopher,Multiscalemodeling Richardson, Casey,Someproblemsinthe Cavallo, Ruggiero, Social welfare maxi- in granular flow mathematics of fracture: Paths from mization in dynamic strategic decision Savva, Nikos, Viscous fluid sheets front kinetics and a level set method problems Shapiro, Yakov, An extension of the Chong, Hamilton, Geometric methods in Hodge theorem to certain non-compact MICHIGAN perceptual image processing manifolds Corbo, Jacomo,Multipartylarge-scale Sidenko, Sergiy, Kac’s random walk and Central Michigan network formation: Economic models coupon collector’s process on posets and mechanisms University (5) Wang, Zuoqin, Spectral properties of Durant, Kathleen, Sentiment drift and its Kähler quotients Department of Mathematics effect on the classification of web log Yang, Fangyun, Dirac operators and posts Alraqad, Tariq, Construction of non- monopoles with singularities embeddability of quasi-residual designs Gu, Jiajun, Bayesian two-way clustering Karthikeyan, Palramani,Compactand Kirsch, Adam, Hash-based data struc- Northeastern Hilbert-Schmidt weighted composition tures for extreme conditions University (3) operators on the Bergman space Lahaie, Sebastien, A modular framework Department of Mathematics Li, Shubiao, The generalized Lagrangian for multi-agent preference elicitation probability distribution: Properties and Ledlie, Jonathan, A locality-aware ap- Long, David, Alexander and Thurston applications proach to distributed systems norms of links and 3-manifolds Osifodunrin, Adegoke Solomon, Investi- Lee, Benjamin, Statistical inference for Pelaez-Menaldo, Jose Pablo, Multiplicative gation of difference sets with order efficient microarchitectural analysis properties of the slice filtration 36

290 NOTICES OF THE AMS VOLUME 56, NUMBER 2 Doctoral Degrees Conferred

Sarker, Animesh,CompactandHilbert- M’Bengue, M’Bagne,Analysisofmodels Lan, Yan, Topics on change-point esti- Schmidt weighted composition opera- for nonlinear dynamic beams with or mation under adaptive sampling proce- tors on the Hardy space without damage or frictionless contact dures Shawash, Nart, Relationships among pop- Lee, Joon Sang, Two stage sequential Michigan State ular interconnection networks and their estimation procedures and a convex University (14) common generalization optimization problem Wijesiri, Galbodayage, Theta functions of Li, Youjuan, Efficient computation and Department of Mathematics algebraic curves with automorphisms model selection of regularized quantile Baykur, Refik Inanc, Symplectic struc- regression tures, Lefschetz fibrations, and their University of Michigan (26) Somboonsavatdee, Anupap, Some contri- generalization on smooth four-mani- Department of Mathematics butions to reliability and lifetime data folds analysis Brooks, Cara, A discrepancy principle Agarwal, Mahesh, p − L function for Verbitsky, Natalya, Associational and for parameter selection in local reg- GSp(4) × GL(2) causal inference in spatial hierarchi- ularization of linear Volterra inverse Bauer, Amy, A multi-scale cell-based cal settings: Theory and applications problems model to simulate and elucidate the Goyt, Adam, Patterns in set partitions mechanisms controlling tumor-induced Wayne State University (5) angiogenesis and compositions Department of Mathematics Guha, Mohar, Front dynamics in non- Cais, Bryden, Correspondences, integral smooth ignition systems in a noisy structures, and compatibilities in p-adic Nguyen, Mau Nam, Variational analysis environment cohomology of marginal functions and set-valued Crown, Sarah, The homology of the cyclic mappings with applications to opti- Gurel, Erhan, Galois structure of modular mization and stability forms of even weight coloring complex of simple graphs Feng, Hualong, Vortex sheet simulations Potsepun, Nadiya, The long-run behavior Lee, Ki-Moon, The maximum-likelihood of the replicator dynamics systems decoding algorithms of low-density of 3D flows using an adaptive triangular panel/particle method under the Stratonovich type random codes over binary erasure channels perturbations Huh, Sukmoon,Modulispacesofstable Lee, Tsung-Lin, A rank-revealing method Sun, Lijing,ACRPoincaré inequality and for low-rank matrices with updating, sheaves on a plane and an embedded curve fundamental solutions of generalized downdating, and applications subelliptic Schrodinger¨ operators Li, Ying, Studies of nonlinear problems Khan, Rizwanur, Non-vanishing of the symmetric square L-function Wei, Jinfeng, Time series modeling for for Maxwell’s equations terrain profiles Luo, Xiaoyue, Local regularization for Maruskin, Jared, On the dynamical propagation of subvolumes and on the Zhu, Chao, Asymptotic properties of nonlinear Volterra integral equation of hybrid stochastic systems Hammerstein type geometry and variational principles of nonholonomic systems Seckin, Elif, Centralizers of elements of Western Michigan prime order in locally finite simple Min, Hyekyung, Stochastic control mod- (2) groups els of optimal dividend and capital University financing Sun, Yuhui,Mathematicalmodelingof Department of Mathematics images and surfaces Mueller, Charles, On the varieties of pairs of matrices whose product is symmetric Cengiz, Nesrin, What allows teachers to Walia, Rajeev, Tensor factorization and extend student thinking during whole spin construction for Kac-Moody alge- Rong, Feng, Critically finite maps, attractors and local dynamics group discussions bras Cox, Dana, Understanding similarity: Sargsyan, Khachik, First passage times in Yu, Si-Ning, Matched interface and bound- Bridging visual and analytical strate- the near-continuum limit of birth-death ary (MIB) method for surface singulari- gies for proportional thinking ties and its applications processes Stein, Andrew, Mathematical models for Department of Statistics and glioblastoma invasion in vitro MINNESOTA Probability Stipins, Janis III,Onfinitek-nets in the complex projective plane Zhang, Yanwei, A hierarchical Bayesian University of approach to model spatially correlated Veomett, Ellen, The computational com- Minnesota-Twin Cities (10) plexity of convex bodies binary data: With applications to dental Division of Biostatistics, School of research Wildrick, Kevin, Quasisymmetric param- eterizations of two-dimensional metric Public Health Michigan Technical spaces Cui, Yue, Smoothing analysis of variance University (1) Zupunski, Eric, A bound on the com- and extending the definition of degrees plexity of the JSJ decomposition in the of freedom Department of Mathematics and bounded case Science School of Statistics Department of Statistics Qin, Huaizhen, Statistical approach for Borba de Andrade, Bernardo,Topicsin genome-wide association study and Amirall, Daniel, Towards assessing time- nonstandard probability theory microarray analysis varying causal effect moderation in Dong, Yingwen, Inference and model experimental and observational studies selection Oakland University (4) Breto, Carles, Statistical inference for Ferrari, Davide, Maximum Lq-likelihood nonlinear dynamical systems Department of Mathematics and method: Parametric density estimation Culp, Mark, Multi-view learning with via nonextensive entropy minimization Statistics additive models on graphs Forzani, Liliana, Sufficient dimension Kirkwood, Daniel,Ahybridalgorithmfor Culp, Stacey, Nonlinear dimensionality reduction based on normal and Wishart the common real zero problem reduction for functional data inverse models

FEBRUARY 2009 NOTICES OF THE AMS 291 Doctoral Degrees Conferred

Kraker, Jessica, Penalized regression Zhao, Bo, Noncommutative differential Department of Statistics methods and validation, with partic- calculus from the inner derivation ular focus on chemometric data Schmid, Kendra, Analysis of landmark data using multi-dimensional regres- Lin, Chihche, Optimal combining of sta- sion tistical procedures MONTANA Shao, Yongwu, Topics on dimension Wang, Yi, Semiparametric mixed-effects reduction Montana State analysis on PK/PD models using differential equations Strief, Jeremy, Bayesian sampling weights: University-Bozeman (3) An approximation to the Polya poste- Department of Mathematical rior Sciences Zhang, Yongli,Modelselection NEW HAMPSHIRE Colt, Diana, Cognitive presence among MISSOURI mathematics teachers: An analysis of University of New tasks and discussions in an asyn- Hampshire (1) chronous online graduate course Missouri University of Harper, Jonathan, The use of computer Department of Mathematics and Science & Technology (2) algebra systems in a procedural algebra Statistics Department of Mathematics and course to facilitate a framework for procedural understanding Fang, Junsheng, Unitarily invariant norms Statistics and tensor products of maximal injec- Sharp, Julia, New statistical methods for tive von Neumann subalgebras Beane, Robbie, Inverse limits of permuta- analyzing proteomics data from affinity tion maps isolation LC-MS/MS experiments Sanyal, Suman, Stochastic dynamic equations University of Montana - NEW JERSEY Missoula (3) University of New Jersey Institute of Department of Mathematical (11) (4) Missouri-Columbia Sciences Technology Department of Mathematics Department of Mathematical Lambert, Scott, Spectral preserver prob- Borovyk, Vita, Box approximation and lems in uniform algebras Sciences related techniques in spectral theory Laobeul, N’Djekornom, Regularization Chandrasekaran, Lakshmi,Roleofplas- El Hitti, Samar, Algebraic resolution of methods for ill-posed Poisson imag- ticity in temporal coding of neuronal formal ideals along a valuation ing problems networks Hanumanthu, Krishna, Toroidalization of VanSpronsen, Hillary, Proof processes of Ha, Joon, Roles of gap junctions in locally toroidal morphisms novice mathematics proof writers neuronal networks Hart, Derrick, Exploration of geometric combinatorics in vector spaces over Murisic, Nebojsa, Instabilities of volatile finite fields NEBRASKA films and drops Koucherik, Elena, Transference and Szego’s¨ Posta, Filippo, Signal transmission in Theorem for measure preserving repre- University of epithelial layers sentations Nebraska-Lincoln (12) Pogan, Alexandru Alin, Dichotomy theo- Princeton University (9) Department of Mathematics rems and applications Department of Mathematics Schlieper, Jared, Extremal sections of unit Davis, Jennifer, Algebraic geometric codes ball in Lorentz sequences space on anticanonical surfaces Arguin, Louis-Pierre, The structure of cor- Wright, Matthew, Boundary value prob- Dvorak, Matthew, Qualitative and quan- relation in quasi-stationary competing lems for the Stokes system in Lipschitz titative analysis of a fluid-structure particle systems domains interactive partial differential equation Carlsson, Erik, Vertex operators and Zymonopoulou, Maria-Isavella,Sections model moduli spaces of sheaves of complex convex bodies Eubanks-Turner, Christina,Primeideals Gornik, Bojan, Duality of Khovanov- in low-dimensional mixed polynomial/ Department of Statistics Rozansky link homology power series rings Juhasz, Andras, Floer homology and Arab, Ali, Hierarchical Bayesian semi- Feller, Heidi, Solving boundary value sutured manifolds parametric zero-inflated Poisson mod- problems using critical point theory ∗ Li, Ye, Smoothing Riemannian metrics in els for multivariate spatio-temporal Gregg, Martha, C -extreme points in the dimension 4 and its applications environmental processes generalized state space of a commuta- He, Xin, Regression analysis of panel tive C∗-algebra Sorrentino, Alfonso, On the structure of count data with dependent observation Higgins, Raegan, Oscillation theory of action-minimizing sets for Lagrangian times dynamic equations on time scales systems Luckas, Melissa, Ranks and bounds for Sullivan, Blair D., Extremal problems in (4) Washington University indecomposable modules over one- digraphs Department of Mathematics dimensional Noetherian rings Xu, Chenyang, Topics on rationally con- ∗ Blanchard, Jeffrey, Existence and ac- Milan, David, C -algebras of inverse nected varieties semigroups curacy results for composite dilation Program in Applied Computational wavelets Sakuntasathien, Sawanya, Global well- Mathematics Lee, Lina, Asymptotic behavior of invari- posedness for systems of nonlinear ant metrics wave equations Kryazhimskiy, Sergey, Pathogen evolu- Maurizi, Brian, Noise sensitivity of an Weiss, Jacob, Second order dynamic equation under natural selection: The influ- entropy-based signal receiver tions on time scales enza A case study

292 NOTICES OF THE AMS VOLUME 56, NUMBER 2 Doctoral Degrees Conferred

Rutgers Li, Qi, Energy functionals and their appli- Graduate Center, City University-Newark (1) cations to Monge-Ampère equations University of New York (7) Mezhericher, Borislav, Computational as- Department of Mathematics and PhD Program in Mathematics pects of Maass forms for SL(3,z) Computer Science Swinarski, David, Geometric invariant Munn, Michael, Volume growth and the McDonald, Keith Tim,Onp-adic zeta theory and moduli spaces of pointed topology of manifolds with nonnegative functions and their derivatives at s =0 curves Ricci curvature Nechayeva, Marina, Asymptotics of To, Tung, A free boundary problem for weighted lattice point counts inside the evolution p-Laplacian equation with NEW MEXICO dilating domains a combustion boundary condition Serme, Abdramane, On iterative refine- New Mexico State Yuan, Xinyi, Equidistribution theory over ment/improvement of the solution to University, Las Cruces (1) algebraic dynamical systems an ill conditioned linear system Department of Mathematical Zhang, Bei, Fourier-Jacobi coefficients of Wojciechowski, Radoslaw, Stochastic com- Eisenstein series on unitary group Sciences pleteness of graphs Zickert, Christian,Hyperbolic3-manifolds Won, Dong Wook,Wordproblemson Noussi, Hubert, Stabilization of compe- and the Cheeger-Chern-Simons class balanced semigroups and groups tition models in the chemostat via Yuan, Shenglan, Dynamics of certain feedback linearization Department of Statistics families of transcendental meromorphic functions Abayomi, Kobi Ako,Diagnosticsformul- University of New Zyman, Marcos, IA-automorphisms and tivariate imputation copula based in- Mexico (2) localization of nilpotent groups dependent component analysis and a Department of Mathematics and motivating example New York University, Statistics Lee, Yi Hsuan, Contributions to the Courant Institute (20) Beznosova, Oleksandra, Bellman func- statistical analysis of item response tions, paraproducts, Haar multipliers, time in educational training Courant Institute of Mathematical andweightedinequalities Sciences Gomez, Ralph, On Lorentzian Sasaki- Cornell University (12) Bramham, Barney, Pseudoholomorphic Einstein geometry Center for Applied Mathematics foliations for area preserving disc maps Cousot, Laurent, Constructions of martin- NEW YORK Lyles, Danielle, Chromaffin cell excitabil- gales and of increasing processes with ity and BK channel gating: Data, model- constrained marginal distributions Clarkson University (4) ing, simulation, and experiment Diaz-Alban, Jose, The high frequency and inviscid limit of acoustic waves in a Department of Mathematics and Robinson, Michael, Eternal solutions and heteroclinic orbits of a semilinear para- porous medium Computer Science bolic equation Fish, Joel, Compactness results for pseudo- Santitissadeekorn, Naratip, Transport Schmidt, Deena, A mathematical look at holomorphic curves analysis and motion estimation of dy- DNA regulatory sequence evolution Hammond, David, Representing and mod- namical systems of time-series data eling images with multiscale local ori- Sherwood, William Erik,Responsein entation Shen, Xunyang, Towards a practical so- networks of bursting neurons: Modeling lution of handling over/under flow central pattern generators Hasha, Alexander, Gravity wave refrac- exceptions with alternate number for- tion by three-dimensionally varying mats Yamada, Richard Yujiro, Quantitative winds and the global transport of models of transcriptional elongation Vora, Mehul, A novel approach to data angular momentum in the atmosphere mining: GA for feature selection Zhang, Wenjie, Measure of serial de- Heymann, Matthias,Thegeometricmin- Yao, Chen, Modeling low-dimensional pendence and testing for conditional imum action method: A least action submanifolds in dynamical systems quantile models principle on the space of curves Hryniewicz, Umberto, Finite energy folia- Columbia University (16) Department of Mathematics tions of convex sets in R4 Department of Mathematics Eshmatov, Farkhod,TheCalogero-Moser Huang, Shih-Ting,Onthemechanismof correspondence for noncommutative forward motion during flapping flight: Baldwin, John, Heegaard Floer homology, deformations of Kleinian singularities Numerical simulation by the immersed contact structures, and open books boundary method Gyrya, Pavel, Heat kernel estimates for Faber, Alexander, Topics in arithmetic Kadota, Minoru, The Madden-Julian os- inner uniform subsets of Harnack-type geometry over function fields cillation and its seasonal impact on Dirichlet spaces Gillam, William, Hyperelliptic Gromov- mid-latitude weather predictability Witten theory Johnston, Henri, The trace map and Galois Kargin, Vladislav, Limit theorems in free module structure of rings of integers Gkigkitzis, Ioannis, On the cross curvature probability theory for absolutely abelian number fields tensor and the cross curvature flow Koiller, José, Invariant measures for cou- Hanson, Nels, Sobolev norms of holo- Schweig, Jay, Poset convex-ear decom- pled map graphs morphic sections and variations of the positions and applications to the flag Kuptsov, Alexey, REM universality for density of states h-vector random Hamiltonians Hsieh, Ming-Lun,Constructionofp-adic Sinefakopoulos, Achilleas, On some classes Lee, Pilhwa, The immersed boundary ordinary Eisenstein series on certain of Borel fixed ideals and their cellular method with advection-electrodiffusion unitary groups resolutions Royfman, Roman, Randomly trapped ran- Kontorovich, Alex, The hyperbolic lattice Velasco, Mauricio Fernando, Monomial dom walks point count in infinite volume with resolutions and the Cox rings of del Shen, Haiping, Two PDE problems from applications to sieves Pezzo surfaces electromagnetics

FEBRUARY 2009 NOTICES OF THE AMS 293 Doctoral Degrees Conferred

Spagnolie, Saverio,Flapping,ratcheting, Loftus, John, Powers of words in language Polishchuk, Valentin, Non-crossing paths bursting and tumbling: A selection families and minimum-cost flows in polygonal of problems in fluid-body interaction Millan-Vossler, Silvia, The Whitehead and domains dynamics the lower algebraic K-theory of braid Tung, Lin, The impact of genotype mis- Stechmann, Samuel, Models of convec- groups on S2 and RP 2 classification errors on the power to tively coupled waves in the tropical Wassink, Bronlyn, Subgroups of R. Thomp- detect a genetic association and gene- atmosphere son’s group F that are isomorphic to environment interaction with Cox pro- Tice, Ian, Lorentz space estimates and F portional modeling applied boundary current dynamics for Wang, Shuqiang, Solving elliptic interface Ginzburg-Landau State University of New problem using mixed finite element Vilensky, Yevgeny, Large deviation bounds York at Buffalo (5) method Wu, Xiangfeng, Optimal designs for seg- for the totally asymmetric simple ex- Department of Mathematics clusion process mented polynomial models and web- Han, Xiaoying, Interlayer mixing in thin based implementation of optimal de- Polytechnic University (3) film growth sign software Zhang, Yue, Path analysis of multivari- Department of Mathematics Li, Jinglai, Estimating the reliability of optical fiber communication systems ate time series data with subject-level Centonze, Paolina, An algebra for access Mastroberardino, Antonio, Three-dimen- covariates control sional equilibrium crystal shapes with Department of Mathematics Lenchner, Jonathan, Sylvester-Gallai re- corner energy regularization An, Daniel, Complete set of eigenfunc- sults and other contributions to combi- Yu, Chih-Chien, Conditions for the exis- tions of the quantum periodic Toda natorial and computational geometry tence of a steady state solution for a chain Morgan, Thomas, Concentration and competition system of plankton popu- Chen, Je-Wei, Neighborly properties of sparsity in space and frequency lation simple convex polytopes Rensselaer Polytechnic Department of Biostatistics Chen, Xiaojun, On general chain model of the free loop space and string topology Institute (7) Pak, Youngju, Multivariate linear path models Dupont, Emiko, A symplectic isotopy of a Department of Mathematical product of projective spaces Sciences State University of New Dutta, Satyaki, Rigidity of conformally York at Stony Brook (31) compact manifolds Agius, Phaedra, Mathematical models for Kalafat, Mustafa, Self-dual metrics on biological data Department of Applied Mathematics 4-manifolds Andersen, Timothy, Trapped slender vor- and Statistics Li, Tao, A monotonicity conjecture for tex filaments in statistical equilibrium Brady, Christine, Power analysis of finite the entropy of Hubbard trees Dediu, Simona,Analysisoffrequency mixtures of Poisson distributions Mustopa, Yusuf,Theeffectiveconeon dependent attenuation in shallow water Braunstein, Janet, Analysis of task map- symmetric powers of curves Gershgorin, Boris, Characterization of ping for parallel supercomputers Prince, Tanvir,OntheLego-Teichmuller¨ thermalized Fermi-Pasta-Ulam chains Du, Jian, Simulations of magnetohydro- game for finite G cover Kunapuli, Gautam, A bi-level optimiza- dynamics multiphase flow Shu, Yu-Jen, Compact complex surfaces tion approach to machine learning Fazzari, Melissa, Classification ensembles and cscK metrics Yan, Fu,Two-stageNashequilibrium with applications to genomics Unal, Ibrahim, Phi-critical submanifolds problems Huang, Zhuying,Thepoweroflink- and convexity in calibrated geometry Zhao, Jinye, Recent applications of Nash age analysis of a quantitative disease equilibria endophenotype Syracuse University (5) Ji, Chen, Joint analysis of gene and Department of Mathematics State University of New protein data Adamowicz, Tomasz, On the geometry of York at Albany (2) Jia, Xicheng, Applications of front track- p-harmonic mappings Department of Mathematics and ing to multiple scientific problems Dickerson, David, High school mathe- Statistics Lavergne, Paul, Thermonuclear flame matics teachers’ understandings of the studies in rectangular geometry purposes of mathematical proof Clark, Timothy, Poset resolutions of Lee, Hyunsun, Compressible multiphase Kimani, Patrick, Calculus students’ un- monomial ideals multispecies flow models derstandings of the concepts of func- Madsen, Alpheus,Symbolicpowersand Li, Yuanhua, Enhanced 3D front tracking tion transformation, function composi- Gorenstein grade-3 ideals method with locally grid based interface tion, function inverse, and the relation- Lim, Noha, Classification ensembles from ships among the three concepts State University of New random partitions using logistic regres- Nzuki, Francis, Investigating African Amer- York at Binghamton (6) sion models ican students’ identity and agency in Ma, Yeming, Step density function and a mathematics and graphing calculator Department of Mathematics and environment at a low-SES school Science bootstrap resampling Manu, Manu, Canalization of gap gene Struble, Dale, Wavelets on manifolds and Atanasov, Risto,Groupsofgeometric expression during early development in multiscale reproducing kernel Hilbert dimension 2 Drosophila melanogaster spaces Chen, Cuixian, Asymptotic properties Masser, Thomas, Breaking temperature University of Rochester (7) of the Buckley-James estimator for a equilibrium for mixed cell hydrody- bivariate interval censorship regression namics Department of Biostatistics and model McQuown, Joseph,Multi-scale,geomet- Computational Biology Du, Jichang, Covariate-matched estima- ric algorithm for non-parametric data He, Hua, Correcting verification bias in tor of the error variance in nonpara- exploration with an application to ge- the assessment of the accuracy of metric regression nomic data diagnostic tests

294 NOTICES OF THE AMS VOLUME 56, NUMBER 2 Doctoral Degrees Conferred

Wagner-Georger, Lesley, Some skew mod- Braun, Tom, High speed model imple- Tang, Lihua, “Smooth” inference for els for quantal response analysis mentation and inversion techniques for clustered survival data smart material transducers Department of Mathematics Yang, Hongmei, Variable selection pro- Brown, Jonathan, N-symplectic quantiza- cedures for generalized linear mixed Bian, Ji, The pair correlation of zeros of tion models in longitudinal data analysis ξ(k)(s) Cook, James, Foundations of supermath- Yoshizaki, Jun,Useofnaturaltags Liang, Lei, Comparison principle for ematics with applications to N =1 in closed population capture-recapture stochastic heat equations supersymmetric field theory studies: Modeling misidentification Lu, Naiji, Models based on pure birth and David, John, Estimation and shape de- Yu, Miao, Quantitative trait loci (QTL) branching process sign: Analysis and applications mapping with longitudinal traits Milinovich, Micah, Mean-value estimates De Vault, Kristen, Numerical study of two Zhang, Min, Semi-parametric methods for for the derivative of the Riemann zeta- problems in fluid flow: Cavitation and analysis of randomized clinical trials function cerebral circulation and arbitrarily censored time-to-event Xue, Heng, Extensions of stochastic inte- Dillard, Karen, An application of implicit data grals as distributions and applications filtering to water resources manage- to SPDEs ment University of North Gong, Yan, Immersed-interface finite- Carolina at Chapel Hill (24) NORTH CAROLINA element methods for elliptic and elas- Department of Mathematics ticity interface problems Hague, Charles, Cohomology of flag Duke University (13) Grove, Sarah, Optimization problems in the presence of uncertainty varieties and the BK-filtration Department of Mathematics Osborne, Jason, On geometric control de- Jablonski, Michael, Real geometric invari- Belov, Sergei, Breaking in the semiclassi- sign for holonomic and nonholonomic ant theory and Ricci soliton metrics on cal solution of the focusing nonlinear mechanical systems two-step nilmanifolds Schrodinger¨ equation Petersen, Richard, Transformation semi- Lee, Joohee, Mathematical descriptions Gratton, Michael, Coarsening of thin fluid groups over groups of nematic polymers in the monolayer limit films Sweetingham, Kelly, Auxiliary signal de- Narkawicz, Anthony, Cohomology jump- sign for fault detection in nonlinear Lin, Zhi, Passive scalar intermittency in ing loci and the relative Malcev comple- systems random flows tion Wills, Rebecca, When rank trumps pre- Lindley, Brandon S., Linear and nonlinear Nicholas, Michael, A third order numer- cision: Using the power method to shear wave propagation in viscoelastic ical method for 3D doubly periodic compute Google’s pagerank media electromagnetic scattering problems Marangell, Robert, The general quadruple Department of Statistics Robbins, Nicholas,Negativepointmass point formula singularities in general relativity Chang, Sheng-Mao, A stationary sto- Richmond, Edward, Recursive structures Spivey, Joseph,Twistedcohomologyof chastic approximation algorithm for in the cohomology of flag varieties hyperelliptic mapping class groups estimation in GLMM Todd, Abby, Inclusion of a glycogen Xu, Feng, SU(3) structures and special Chiswell, Karen, Model diagnostics for regulation mathematical model into a Lagrangian geometries the nonlinear mixed effects model with contextual metabolic framework balanced longitudinal data Yang, Gao, Short time behavior of so- Department of Statistical Science Griffith, Emily, Catch curve and capture lutions to nonlinear Schrodinger¨ equa- Chu, Jen-Hwa, Bayesian function esti- recapture models: A Bayesian combined tions in N space dimensions mation using overcomplete dictionaries approach Yao, Lingxing, Viscoelasticity at micro- with application in genomics Gu, Jiezhun, Nonparametric and semi- scopic and macroscopic scales charac- Kinney, Satkartar,Modelselectionand parametric inference about ROC curves terization and prediction multivariate inference using data mul- Huang, Lingkang, Variable selection in Department of Statistics and tiply imputed for disclosure limitation multiclass support vector machine and Operation Research and nonresponse application in genomics data analysis Pillai, Natesh, Levy random measures: Jones, Martha,Aretrospectivemethod Bai, Ping, Temporal-spatial modeling in Posterior consistency and applications for inference on haplotype main ef- FMRI Sang, Huiyan, Extreme value modeling fects and haplotype-environment inter- Didier, Gustavo, Adaptive wavelet decom- for space-time data with meteorological actions using clustered haplotypes positions of time series applications Liu, Jiajun, Domain enhanced analysis Gaydos, Travis, Data representation and Shen, Haige, Bayesian analysis in can- of microarray data using the gene basis selection to understand variation cer pathway studies and probabilistic ontology annotations of function valued traits pathway annotation Liu, Shufang, Modeling mean residual life Huang, Tao, Continuous optimization Woodard, Dawn, Conditions for rapid and function using scale mixtures approaches to the quadratic assignment torpid mixing of parallel and simulated Lu, Xiaomin, Improving the efficiency of problem tempering on multimodel distributions test and estimates of treatment effect Lee, Chihoon, Long time asymptotics for with auxiliary covariates in the presence constrained diffusions in polyhedral North Carolina State of censoring domains University (30) Nail, Amy, Quantifying local creation and Lee, Myung Hee, Continuum direction regional transport using a hierarchical vectors in high dimensional low sample Department of Mathematics space-time model of ozone as function size data Beier, Julie, Crystals for Demazure mod- of observed NOx, a latent space-time Liu, Liqiang, Queueing models with ules of special linear quantum affine VOC process, emissions, and meteorol- workload-based balking applications to type ogy call center Beun, Stacy, On the classification of orbits Ni, Xiao, Variable selection in partial lin- Liu, Xuxin, New statistical tools for of minimal parabolic k-subgroups act- ear models and semiparametric mixed microarray data and comparison with ing on symmetric k-varieties of SL(n, k) models existing tools

FEBRUARY 2009 NOTICES OF THE AMS 295 Doctoral Degrees Conferred

Maroulas, Vasileios,Smallnoiselarge Case Western Reserve Nikolov, Martin, Construction of series of deviations for infinite dimensional sto- University (9) degenerate representations for GSp(2) chastic dynamical systems and PGL(n) Shamseldin, Elizabeth C., Asymptotic Department of Mathematics Park, Chongseok, Irregular behavior in an multi-variate kriging using estimated Li, Zhuo Bin, Schistosomiasis transmis- excitatory-inhibitory neural network parameters with Bayesian prediction sion and control in a distributed het- Qi, Dongwen, On irreducible, infinite, methods for non-linear predicaments erogeneous human-snail environment non-affine Coxeter groups Sun, Xing, Significance and recovery of in coastal Kenya Schoenecker, Kevin Joseph, An infinite block structures in binary and real- Zachlin, Paul, On the field of values of family of anticommutative algebras valued matrices with noise the inverse of a matrix with a cubic form Trovero, Michele A., Effects of aggre- Xu, Songyun, Degree 2 curves in the gation on estimators of long-range Department of Epidemiology and Dwork pencil dependence Biostatistics Department of Statistics Zhang, Lingsong, Functional singular Bajunirwe, Francis, Effectiveness of an- value decomposition and multi-resolu- tiretroviral therapy in rural Uganda Cui, Zhenhuan, The solution paths of tion anomaly detection Jun, Gyungah, Identification of genes multicategory support vector machines: Zhou, Jie, High dimensional spatial mod- associated with age-related cataract Algorithm and applications eling of extremes: With application to Kiwanuka, Noah, The effect of HIV-1 Lam, Chen Quin, Sequential adaptive U.S. rainfalls subtypes on HIV transmission and designs in computer experiments for disease progression in Rakai district, response surface model fit University of North Uganda Lang, Lixin, Advancing sequential Monte Carolina at Charlotte (6) Kou, Tzuyung Doug, Watchful waiting Carlo for model checking, prior smooth- and active surveillance in prostate ing and applications in engineering and Department of Mathematics and science Statistics cancer patients—a population-based study using the SEER-Medicare linked Li, Hongfei, Approximate profile likeli- Fan, Kai, A generalized discontinuous database hood estimation for spatial-dependence Galerkin (GDG) method and its applica- Liu, Constance, Evaluating measures of parameters tions geographic accessibility in urban dia- Pan, Xueliang, Using structural informa- Hyun, Jeunggeun, Statistical analysis of betics in Cuyahoga County tion in modeling and multiple align- competing risk models Londono, Douglas, Applications of the ments for phylogenetics Jalali, Mohammadreza,Centrallimitthe- Hardy-Weinberg principle to detection Roberts, Clint, Imputing missing values orem for Markov chains on compact of linkage disequilibrium and genotyp- in time series of count data using abelian groups ing errors in the context association hierarchical models Jeong, Jae-Woo,Implementationofrepro- studies Wang, Ke,Onconcomitantsoforder ducing polynomial particle (RPP) shape Marrie, Ruth Ann, Influence of comor- statistics functions in meshless particle meth- bid diseases and health behaviors on Wei, Lai, Spectral-based tests for period- ods for two-dimensional elliptic partial clinical characteristics, disability at di- icities differential equations agnosis and disability progression in McNair, Dawn, Duals of ideals and trace multiple sclerosis Ohio University, Athens (1) properties in rings with zero divisors Department of Mathematics Kent State University (3) Squartini, Nicola, Global limit theorems Srivastava, Ashish, Rings characterized for sums of independently identically Department of Mathematical by properties of direct sums of modules distributed random variables using qua- Sciences and on rings generated by units sicumulants Abramov, Vilen, Stopping times related to trading strategies University of Akron (1) NORTH DAKOTA Li, Hongcheng, Multivariate extension of Department of Theoretical and CUSUM procedure Applied Mathematics North Dakota State Rollick, Mary Elizabeth, Puzzling over Childers, Carey, Effective properties of University, Fargo (1) spatial reasoning: A phenomenological study of pre-service elementary teach- a fiber reinforced composite with a Department of Mathematics ers functionally graded transition zone Matson, Amanda, Results regarding finite University of Cincinnati (6) generation, near finite generation, and Ohio State University, Department of Mathematical the catenary degree Columbus (18) Sciences Department of Mathematics Camfield, Christopher,ComparisonofBV OHIO Balachandran, Niranjan,The3-design norms in weighted Euclidean spaces problem and metric measure spaces Bowling Green State Hambrock, Richard, Evolution of condi- Hunter, Tina, Gibbs sampling and ex- University (2) tional dispersal: A reaction-diffusion- pectation maximization methods for advection approach Department of Mathematics and estimation of censored values from Hur, Suhkjin, The Kuratowski covering correlated multivariate distributions Statistics conjecture for graphs of order less than Jiang, Dongming, Objective Bayesian test- Marcusanu, Mihaela, The classification of 10 ing and model selection for Poisson 1-embeddable Fullerenes Lennon, Craig, On the likely number of models Yenigun,¨ Deniz, A test of independence stable marriages Oraby, Tamer, Spectra of random block- in contingency tables based on maximal McClain, Christopher, Edge colorings of matrices and products of random ma- correlation graphs and multigraphs trices

296 NOTICES OF THE AMS VOLUME 56, NUMBER 2 Doctoral Degrees Conferred

Ruth, Harry L., Jr., Conformal densities Jordan, Alexander, A super version of Keith, William, Ranks of partitions and and deformations of uniform Loewner Zhu’s theorem Durfee symbols metric spaces Kronholm, William, The RO(G)-graded Rowell, Michael,TheBaileytransform Usman, Muhammad, Forced oscillations Serre spectral sequence and conjugate Bailey pairs of the Korteweg-de Vries equation and Miller, Matthew, The rational homotopy Stojanovic, Gordana, Embedding with their stability types of configuration spaces of three- certain non-degeneracy conditions dimensional lens spaces Wang, Jiakou, Stochastic and determinis- University of Toledo (1) Wilson, James, Group decompositions, tic coagulation models, their numerical Department of Mathematics Jordan algebras, and algorithms for approximations and applications to cell Liu, Nanshan, Theory and applications of p-groups aggregation Legendre polynomials and wavelets Zhang, Ke, Thermodynamic formalism PENNSYLVANIA for maps with inducing schemes OKLAHOMA Department of Statistics Bryn Mawr College (3) Han, Bing, A Bayesian approach to false Oklahoma State Department of Mathematics discovery rate for large scale simulta- University (1) Battiste Presutti, Cathleen, Determining neous inference Department of Statistics lower bounds for packing densities of Hui, Guodong, Matrix distances with non-layered patterns using weighted their application to finding directional Wagler, Amy, Simultaneous inference in templates deviations from normality in high- generalized linear model settings Dalton, Jennifer, Legendrian torus links dimensional data University of Oklahoma (3) Teti, Sherry, The existence of elliptic peri- Jung, Hyekyung, A latent-class selection model for nonignorable missing data Department of Mathematics odic orbits in the smoothed Bunimovich stadium Li, Yan (Maggie), Some contributions to Martinez, Eduardo, Combination of qua- nonparametric modeling with corre- siconvex subgroups in relatively hyper- Carnegie Mellon lated data bolic groups University (6) Seo, Byungtae, Doubly-smoothed maxi- Olaya, Pedro, Orbital integral correspon- mum likelihood estimation Department of Mathematical Science denceforthepair(G2, Sp(1,R)) via the Tang, Zhihui, Three topics on dimension Cauchy Harish-Chandra integral Anthony, Barbara, Approximation algo- reduction Seo, Arim, Torus leveling of (1, 1)-knots rithms for network design with uncer- Yang, Jingyun, Measurement of agree- tainty ment for categorical data OREGON Carita, Graca, Relaxation in SBV for Yao, Weixin, On using mixtures and constrained-valued fields modesofmixturesindataanalysis Oregon State University (5) Cohen, Albert, A probabilistic analysis of Young, Derek,Astudyofmixturesof Department of Mathematics grain growth regression Towsner, Henry,Someresultsinlogic Strowbridge, Jessica, Middle school teach- and ergodic theory Temple University (4) ers’ use of a formative feedback guide Young, Michael, Triangle problems in Department of Mathematics in mathematical problem solving in- extremal graph theory struction Bitew, Worku, Sufficient conditions and Department of Statistics Department of Statistics higher-order regularity for local mini- mizers in the calculus of variations Serban, Mihaela, Derivative pricing under Giovanini, Jack, Generalized linear mixed DeSario, David, Polyhedral sums and models with censored covariates multivariate stochastic volatility models with application to equity options theta series Henry, John, III, Extreme value index Elhashash, Abdul Rahman (Abed), Perron- estimation with applications to model- Lehigh University (3) Frobenius properties of general matri- ing extreme insurance losses and sea ces and generalized M-matrices which Department of Mathematics surface temperatures may not have nonnegative inverses Irvine, Kathi, Graphical models for multi- Gorman, Jennifer, Nested traveling sales- Liu, Zhongzhi, Quantum random walks variate spatial data person problems under decoherence Lu, Lin, Unconditional estimating equa- Mformbele, Akongnwi Clement,Timede- tion approaches for missing data pendent and steady state interaction University of among capillaries in skeletal muscle Pennsylvania (4) Portland State Panofsky, Ellen, Graph labeling problems Department of Mathematics University (2) with distance conditions Department of Mathematics and Bogdan Pavelescu, Elena,Braidsandopen Statistics Pennsylvania State book decompositions University (18) Dalakov, Peter, Higgs bundles and opers Ciancetta, Matthew, Statistics students’ Fithian, David, Pseudomodular Fricke reasoning when comparing distribu- Department of Mathematics groups tions of data Bang, Seunghoon, Rarefaction wave of Kerin, Martin, Biquotients with almost Noll, Jennifer, Graduate teaching assis- pressure-gradient system positive curvature tants’ statistical knowledge for teaching Barton, James, Generalized complex structures on Courant algebroids University of Oregon (5) University of Pittsburgh, Cho, Durkbin, Multilevel methods for Pittsburgh (7) Department of Mathematics the generalized finite element method Department of Mathematics Archey, Dawn, Crossed product C∗- discretizations algebras by infinite group actions with Kang, Hunseok,Dynamicsofthelocal Day, Jerry, On Banach function spaces a generalized tracial Rokhlin property map of a discrete Brusselator model and the fixed point property

FEBRUARY 2009 NOTICES OF THE AMS 297 Doctoral Degrees Conferred

Day, Judy, Mathematical approaches to Wang, Wei, Multiscale discontinuous Department of Statistics modeling, understanding, and control- Galerkin methods and applications Adekpedjou, Akim, Estimation of the gap- ling the acute inflammatory response time distribution with recurrent event to pathogen and endotoxin SOUTH CAROLINA data under an informative monitoring Hancioglu, Baris,Mathematicalmodeling period of virus dynamics in immunology Clemson University (6) Autin, Melanie, Nonparametric methods Mi, Qi, Modelling wound healing in Department of Mathematical in the analysis of estuarine water necrotizing enterocolitis and diabetic Sciences quality data foot ulcer Beeler, Robert, Automorphic decomposi- Deutsch, Roland, Benchmark analysis for Neda, Monika, Numerical analysis and two predictor variables phenomenology of homogeneous, iso- tions of graphs Ignatova, Iliana, Multistage samples and tropic turbulence generated by higher Faulkner, Bryan,Estimatesrelatedtothe the minimum sum method for Medicare order models of turbulence arithmetic of elliptical curves fraud investigations Pejić, Bojana, On the uniqueness of Polish Howell, Jason, Numerical approxima- Ni, Jun, Extensions of hierarchical Bayesian group topologies tion of shear-thinning and Johnson- Segalman viscoelastic fluid flows shrinkage estimation with applications Xie, Dejun, Optimal prepayment strategy to a marketing science problem of mortgages Kraft, Christine, Planning, scheduling, and timetabling in a university setting Quiton, Jonathan, General outlier detec- Seneviratne, Padmapani, Permutation de- tion and goodness of fit for recurrent RHODE ISLAND coding of the codes from graphs and event data designs Zhang, Litong, The estimation of multi- Brown University (15) Zhao, Meng, Issues in model selection, dimensional item response theory model Department of Mathematics minimax estimation, and censored data analysis Kwon, Hyun-Kyoung, Similarity of op- TENNESSEE erators and geometry of eigenvector Medical University of University of Memphis (2) bundles South Carolina (7) Department of Mathematical Miller, Stephen Francis, The calculus of Department of Biostatistics, Sciences equivariant spectra and a classification Bioinformatics & Epidemiology of degree 2 endofunctors Wheeler, Jeffrey Paul, The Cauchy-Daven- Stange, Katherine Elisabeth, Elliptic nets Hedden, Sarra, Methods in substance abuse clinical trials port theorem and the Erdos-Heilbronn˝ and elliptic curves problem for finite groups Wise, Jonathan Samuel Dennis, The genus Howard, Virginia, Nativity and interstate migration patterns and their effect on Zhang, Lijun, Stochastic and state space zero Gromov-Witten theory of [Sym2P2] stroke risk factors models of carcinogenesis with applica- and the enumerative geometry of hy- tions perelliptic curves in P2 Jaffa, Miran, Development and application of models for slope estimation for Yasufuku, Yu, Vojta’s conjecture and univariate and bivariate longitudinal University of Tennessee, blowups outcomes in the presence of informa- Knoxville (2) tive right censoring Division of Applied Mathematics Department of Mathematics Johnson, Shayna, Racial disparities in Chun, Sehun, High-order accurate meth- living kidney donations among South LaGrange, John, Zero-divisor graphs, ods for solving Maxwell’s equations; Carolinians: The effect of health con- commutative rings of quotients, and modeling photonic crystals and thin ditions, individual behavior, and family Boolean algebras layer approximations attributes Phillippi, R. David, A comparison of the Dean, Thomas Anthony, A subsolutions Karpievitch, Yuliya, Computational tools deck group and the fundamental group approach to the analysis and imple- for MS-based proteomics of uniform spaces obtained by gluing mentation of splitting algorithms in Mountford, William, Racial variation in rare event simulation long-term risk of cardiovascular disease Vanderbilt University (7) Feiszli, Matt, Conformal shape represen- mortality with regards to diabetes and Department of Mathematics tation hypertension Foo, Jasmine, Multi-element probabilistic Rastogi, Amal, Arterial compliance and Callender, Hannah,Mathematicalmod- collocation in high dimensions: Appli- periodontal inflammation in adults eling of species-specific diacylglycerol cations to systems biology and physical dynamics in the RAW 264.7 macrophage systems University of South following P2Y6 receptor activation by Keaveny, Eric, Dynamics of structures Carolina (12) uridine 5 -diphosphate in active suspensions of paramagnetic Department of Mathematics Hinow, Peter, Partial differential equa- particles and applications to artificial tion models for intranuclear diffusion, micro-swimmers Jordan, Kelly, The necklace poset is a inverse problems in nanobiology and Leder, Kevin, Large deviations and impor- symmetric chain order cell cycle specific effects of anticancer tance sampling for queueing systems Kozek, Mark, Applications of covering drugs with discontinuous service policies systems of integers and Goldbach’s Jennings, David, Topological algebras and Li, Zheng, Approximation to random conjecture with monic polynomials q-undemanding varieties process by wavelet basis Owens, Luke, Multigrid methods for two Lambert, Thomas Paul, On the classifica- Libertini, Jessica, Determining tumor weakly over-penalized interior penalty tion of closed flat four-manifolds blood flow parameters using dynamic methods Nowak, Piotr Wojciech, Property A as imaging data Rusu, Anamaria, Determining starlike metric amenability and its applications bodies by their curvature integrals Micheli, Mario, The differential geometry to geometry of landmark shape manifolds: Metrics, Sanacory, Frank, The richness of the Spakula, Jan, K-theory of uniform Roe geodesics, and curvature space of operators on a Banach space algebras

298 NOTICES OF THE AMS VOLUME 56, NUMBER 2 Doctoral Degrees Conferred

Yattselev, Maxym Leonidovich,Non-Hermi- Southern Methodist Texas Tech University (6) tian orthogonality and meromorphic University (5) Department of Mathematics and approximation Department of Mathematics Statistics TEXAS Cao, Guanghua (Kenny),Pricingandrisk Cupidon, Jean Rene, Functional data management of variable annuities and analysis Baylor University (2) equity indexed annuities Ji, Xiao Yi,Fréchet differentiation of functions of operators with application Department of Mathematics Chaturvedi, Praveen, Single phase multi- component flow simulation in porous to functional data analysis Jackson, Billy Joe,Agenerallinearsys- media Pang, Wai Kong Johnny, Some statistical methods for directly and indirectly tems theory on time scales: Transforms, Lam, Kwan, Pattern formation in non- observed functional data stability, and control linear chemical systems Rogers, James W., Adaptive methods for Talukder, Mohammed H., Order-restricted the Helmholtz equation with discontin- Department of Statistics Science analysis for repeated measures uous coefficients at an interface Wang, Keyi, Variance reduction methods Robertson, Steve, Generalizations and applications of linear chirp stationary based on smoothing spline estimator (16) for non-parametric regression model Rice University processes Wesley, Curtis, Discrete time and contin- Department of Computational and Xu, Mengyuan, Filtering analysis of non- uous time epidemic models with appli- Applied Mathematics stationary time series by time deforma- cations to the spread of hantavirus in tion Castillo, Edward, Optical flow methods wild rodent and human populations for the registration of compressible flow images and images containing Texas A&M University (17) University of Houston (5) large voxel displacements of artifacts Department of Mathematics Department of Mathematics Eydelzon, Anatoly,Astudyoncondi- tions for sparse solution recovery in Abbott, Kevin, Applications of algebraic Linsenmann, Christopher, Adaptive multi- compressive sensing geometry to object/image recognition level-based shape optimization for sta- McClosky, Benjamin, Independence sys- Bondarenko, Ievgen, Groups generated by tionary Stokes flows by path-following tems and stable set relaxations bounded automata and their Schreier primal-dual interior point methods graphs Turner, Jesse, Multi-scale behavior in Gucciardi, Barbara,Subgroupoidsincou- chemical reaction systems: Modeling, Celik, Mehmet, Contributions to the com- pled cell systems applications, and results pactness theory of the ∂ Neumann Hao, Jiao, Numerical methods and sim- Young, Joseph, Program analysis and operator ulations for fluid/particle interactions: transformation in mathematical pro- Dobrev, Veselin, Preconditioning of dis- Sedimentation in a viscoelastic fluid gramming continuous Galerkin methods for sec- and cell lifting in shear flow ond order elliptic problems Nguyen, Ha, Whitney regularity for solu- Department of Mathematics Dostert, Paul, Multiscale simulation meth- tions to the Livsic coboundary equation Jennings, Landan, Sufficient conditions ods for stochastic porous media flows on Cantor sets in dimension three for Hamiltonian paths and applications Patel, Swabhimita,Globalexistencefor Jorgensen, Jamie, Surface homeomor- Fuselier, Jenny, Hypergeometric func- solutions of diffusively coupled reac- phisms that do not extend to any tions over finite fields and relations to tion diffusion equations handlebody and the Johnson filtration modular forms and elliptic curves Ralston, David, Heaviness: An extension Ivanov, Nikolay, On the structure of some University of North of a lemma of Yuval Peres free products of C∗-algebras Texas (2) Simpson, Matthew, On log canonical mod- Kannan, Lavanya, Densities in graphs Department of Mathematics elsofthemodulispaceofstablepointed and matroids genus zero curves Kostic, Dimitrije,Graphsearchinganda Atim, Alexander, Uniqueness results for generalized parking function the infinite unitary, orthogonal and Department of Statistics associated groups Moreira, Rivera, Products of represen- Pudipeddi, Sridevi, Localized radial solu- Fox, Garrett, A Bayesian hierarchical tations of symmetric group and non- tions for nonlinear p-Laplacian equa- model for detecting associations be- commutative versions tween haplotypes and disease using tion in Rn unphased SNPs Ruffo, James, A straightening law for the Drinfeld Lagrangian Grassmannian Gershman, Jason, Classification of time- University of Texas at Zheng, Bentuo, Embeddings and factor- course gene expression array data Arlington (6) izations of Banach spaces Jabri, Hannah, Term structures and con- Department of Mathematics ditional probabilities of corporate de- Department of Statistics fault in an incomplete information Badiu, Florin, Study of multiple impacts setting Gold, David, Bayesian learning in bioin- of a rigid body with a flat surface Kyj, Lada, Estimating realized covariance formatics Busse, Theresa, Generalized inverse scat- using high frequency data Jin, Lei, Generalized score tests for tering transform for the nonlinear Noyola-Martinez, Josue, Investigation of missing covariate data Schrodinger¨ equation the Tau-leap method for stochastic Lee, Sang Han, Estimating and testing of Martines, Ian, Mathematical analysis of simulation functional data with restrictions allelopathy and resource competition Papkov, Galen, Locally-adaptive polynomial- Liu, Lian, Topics in measurement error models smoothed histograms with application and missing data problems Mo, Min, Estimating absolute transcript to massive and pre-binned data sets Liu, Yingxue, Estimation of circadian pa- concentration for microarrays using Williams, Talithia, A dynamic spatio- rameters and investigation in cyanobac- Langmuir adsorption theory temporal model for real-time estima- teria via semiparametric varying coeffi- Stern, Paul, On progenitively Koszul tion of rainfall data cient periodic models commutative rings

FEBRUARY 2009 NOTICES OF THE AMS 299 Doctoral Degrees Conferred

Xie, Peng, Uniform compact/noncompact Yin, Kunshan, A Bayesian paradigm for Daniels, Inger, Wellposedness of a non- schemes for shock/boundary layer in- method comparison studies linear structural acoustic interaction teraction with a Boussinesq plate equation UTAH Ott, Katharine, Boundary integral equa- University of Texas at tions in non-smooth domains Austin (19) Brigham Young Pons, Matthew, Composition operators on Besov and Dirichlet type spaces Department of Mathematics University (1) Suwanna, Sujin, On the mean square Carreon, Fernando, Singular limits of Department of Mathematics distance in the Anderson model reaction diffusion equations of KPP type in an infinite cylinder Grout, Jason, The minimum rank problem over finite fields Virginia Polytechnic Chan, Chi Hin, The De Giorgi method Institute and State as applied to the regularity theory of University of Utah (8) incompressible Navier-Stokes equations University (9) Cozzi, Elaine, Incompressible fluids with Department of Mathematics Department of Mathematics vorticity in Besov spaces Chamberlain, Erin, Modules with pre- Czubak, Magdalena, Well-posedness for scribed intersection properties Baccouch, Mahboub, Superconvergence the space-time monopole equation and Iwao, Yoshihiro, Invariance of Gromov- and a posteriori error estimation for the Ward wave map Witten theory under a simple flop discontinuous Galerkin method applied Garza, John, The height in terms of the McNulty, Meagan,Mathematicalmodels to hyperbolic problems on triangular normalizer of a stabilizer of respiratory inflammation meshes Ghosh, Rohit, Incompleteness of the Nesse, William, Random fluctuations in Hughes, Sharon, Born Oppenheimer ex- Giulietti-Ughi arc dynamical neural networks pansion for diatomic molecules with Hammond, John, Regular realizations of Song, Qiang, Questions in local cohomol- large angular momentum p-groups ogy and tight closure Temimi, Helmi, A discontinuous Galerkin Hitt, Laura, Genus 2 curves in pairing- Thompson, Joshua, Grafting real complex method for higher-order differential based cryptography and the minimal projective structures equations applied to the wave equation embedding field Todorov, Gueorgui, Pluricanonical map Timsina, Tirtha, Sensitivities in option Klonoff, Kevin, An index theorem in on threefolds of general type and the pricing models differential K-theory Gromov-Witten potential of the local Luxton, Mark, The log canonical compact- Zhang, Dali, Inverse electromagnetic Department of Statistics ification of the moduli space of six lines problem for microstructure media Fraker, Shannon,Evaluationofscan P2 in methods used in temporal monitoring Moreira, Diego, Least supersolution ap- of public health surveillance data proach to regularizing elliptic free VERMONT Lee, Mi Hyun, On independent reference boundary problems University of Vermont (1) priors Samuels, Charles, Auxiliary polynomials and Weil height Department of Mathematics and Li, Zheng-rong, Model-based tests for Statistics standards evaluation and biological as- Van Horn-Morris, Jeremy,Constructions sessments on open decompositions Mahassen, Hania, Weakly and strongly Love, Kimberly, Modeling error in geo- Young, Andrea, Modified Ricci flow on a correlated two-dimensional layered graphic information systems principal bundle Coulomb systems Wan, Wen, A semiparametric method to Institute for Computer Engineering multi-response optimization and Sciences VIRGINIA Bauman, Paul, Adaptive multiscale mod- Old Dominion eling of polymeric materials using goal- WASHINGTON oriented error estimation, Arlequin cou- University (3) pling and goals algorithms Department of Mathematics and University of Cottrell, John, Isogeometric analysis and Statistics Washington (32) numerical modeling of the fine scale Department of Applied Mathematics fields within the variational multiscale Parrish, Sarah, Analysis and application method of perfectly matched layer absorbing boundary conditions for computational Bale, Brandon, Modeling the dynamics Khandelwal, Shweta, Ecology of infec- aeroacoustics and stability of mode-locked fiber lasers tious diseases with contact and perco- Gomez, Miguel, Optimization-based anal- lation theory Sabo, Roy, Modeling and efficient estimation of intra-family correlations ysis of rigid mechanical systems with Sokolova, Ekaterina, Indifference valua- unilateral contact and kinetic friction tion in non-reduced incomplete models Thomas, Howard, II, On the use of quasi- Jeon, Jihyoun,Mathematicalmodeling with a stochastic risk factor Newton methods for the minimization of convex quadratic splines of pre-malignant lesions in multistage Su, Qimou, Essays on derivatives pricing carcinogenesis in incomplete financial markets University of Virginia (6) Patterson, Matthew, Computing the Abel University of Texas at Department of Mathematics map and the Riemann constant vector Seo, Gunog, The dynamics of sim- (2) Bociu, Lorena, Existence, uniqueness and Dallas ple predator-prey models with Holling blow-up of solutions to wave equations Department of Mathematical functional responses with supercritical boundary interior Sciences sources and damping Srivastava, Santosh, Bayesian minimum Sahi, Ramanjit, Tangle replacement moves Cramer, Wesley, Cyclotomic Specht filtra- expected risk estimation of distribu- on links tions and Delta filtrations tions for statistical learning

300 NOTICES OF THE AMS VOLUME 56, NUMBER 2 Doctoral Degrees Conferred

Department of Biostatistics Washington State Tang, Yudong, Geodesic rays and test configurations Chen, Lin, Causal modeling in quantita- University (2) Wang, Bing, On the conditions to extend tive genomics Department of Mathematics Ricci flow French, Benjamin, Analysis of aggregate Hsu, Chia-Yu, A 3D bacterial swimming Wang, Jue, On lower branch exact coher- longitudinal data with time-dependent ent structures exposure model coupled with external fluid mechanics using the immersed boundary Huang, Yang, Evaluating the predictive- method University of Wisconsin, ness of continuous biomarkers Jeon, Jong-Sam, Powerful ray patterns Milwaukee (9) Hubbard, Rebecca, Modeling a non- homogeneous Markov process via time Department of Mathematical transformation WEST VIRGINIA Sciences Leek, Jeffrey, Surrogate variable analysis Dudek, John, A mathematical investiga- Rosenthal, Elisabeth,Linkageandsegre- West Virginia tion of solutions for the two-component gation analysis allowing for multiallelic University (4) order parameter in the Ginzburg- Landau equations of superconductivity inheritance Department of Mathematics Rudser, Kyle,Variableimportanceinpre- Lee, Jae Kook, Some covers and relative dictive models: Separating borrowing Cai, Maomao, Solutions for a 2-dimen- covers of modules information and forming contrasts sional stabilized Kuramoto-Sivashinsky Lehrke, Stephen, Asymptotic properties system of the MLE of parameters of the Taylor, Leslie, Estimating causal treat- multivariate O-U process ment effect in randomized clinical Sutyak, Andrea, Pierce-Engel hybrid ex- trials with noncompliance and outcome pansions May, Margaret, Finite dimensional Z- nonresponse Van Vliet, Daniel, Nonlinear approxima- compactifications tion using Blaschke polynomials Mooney, Christopher, On boundaries of Yu, Xuesong, Statistical methods for ana- CAT(0) groups lyzing genomic data with consideration Zhang, Taoye, Integer flow and Petersen 2 of spatial structures minor Schroeder, Timothy, l -homology of Cox- eter groups Department of Mathematics Sears, Christopher, Monotonicity of knead- WISCONSIN ing sequences in families of one-kink Bahuaud, Eric, Intrinsic characterization maps of asymptotically hyperbolic metrics Medical College of Shomberg, Asta, Estimation of false dis- Courdurier, Matias, Restricted measure- Wisconsin (2) covery rate under parametric assump- ments for the X-ray transform Division of Biostatistics tions with application to DNA micro- Dochtermann, Anton,Thetopologyof arrays graph homomorphisms Liu, Jingxia, Utilizing propensity scores Zaidan, Younis, Analysis of Maxwell- Eroglu, Ilgar, Self-similar sets, projec- to test treatment effects in survival systems with various nonlinear polar- tions and arithmetic sums data ization mechanisms Zhang, Yinghua, Selecting between the Frohmader, Andrew, Face vectors of flag Cox and Aalen models for right cen- complexes sored survival data Kelly, Elizabeth, Schubert objects Kissel, Kris, Generalizations of a result of University of Wisconsin, Lewis and Vogel Madison (13) Krishnan, Venkateswaran, A support the- Department of Mathematics orem and an inversion formula for the geodesic ray transform Deng, Geng, Simulated-based optimiza- Langmore, Ian, Inverse transport with tion angularly averaged measurements Henderickson, Anders, Supercharacter Warren, Micah, Special Lagrangian equa- theories of finite cyclic groups tions Holden, Christopher,Mod4Galoisrepre- Williams, Catherine, Asymptotic behavior sentations and elliptic curves of marginally trapped tubes in spheri- Hunter, James, Higher-order reverse topol- cally symmetric black hole spacetimes ogy Yun, Sangwoon, A coordinate gradient Kieserman, Noah, The Liouville phe- descent method for structural non- nomenon in the deformation problem smooth optimization of coisotropics Mueller, Stefan, The group of Hamiltonian Department of Statistics homeomorphisms and co-symplectic topology Berrocal, Veronica, Probabilistic weather Raghavan, Dilip, Madness and other forecasting with spatial dependence topics in set theory Mondal, Debashis, Wavelet variance anal- Rose, Michael, On Gromov-Witten invari- ysis for time series and random fields ants of stacks Oron, Assaf, “Up-and-down” and the Rouse, Jeremy, Arithmetic analytic and percentile-finding problem geometric aspects of the theory of Pavlides, Marios, Nonparametric estima- modular forms tion of multivariate monotone densities Shallue, Andrew, Two number theoretic Telesca, Donatello, Bayesian hierarchical algorithms that illustrate the power and curve registration limitations of randomness

FEBRUARY 2009 NOTICES OF THE AMS 301 American Mathematical Society HeadlinesHeadlines &DeadlinesDeadlines a members-only email news service Headlines Fields Medalists AMS Prizes and Awards Deadlines In Memory Of...& News from Math Institutes Calls for Proposals AMS Sectional Meetings Meeting Registration Centennial Fellowships Deadlines Reports on Special Events Calls for Nominations Annual List of Doctorates Application Deadlines Joint International Meetings NSF Announcements Links to News Releases on Mathematics Math in the Media

Twice-a-month email notifications of news, announcements about programs, publications, and events, as well as deadlines for fellowship and grant applications, calls for proposals, and meeting registrations.

AMS members can sign up for the service at www.ams.org/enews AMERICAN MATHEMATICAL SOCIETY Associate Treasurer

The American Mathematical Society is seeking applications and nominations of candidates for the post of Associate Treasurer. An Associate Treasurer is an officer of the Society and is appointed by the Council to a two-year term, ordinarily beginning on 01 February. In this case the term will begin as soon as possible and end 31 January 2012. Reappointments are possible and desirable. All necessary expenses incurred by an Associate Treasurer in performance of duties for the Society are reimbursed, including travel and communications.

Duties

The primary responsibilities of an Associate Treasurer, like those of the treasurer, are to administer or to supervise the administration of fiscal policies laid down by the Trustees. To monitor the receipt and expenditure of funds and the care of investments. To monitor budgets and trends of finance over periods of years. To review salary policy and its applications to individuals. The Associate Treasurer has all the duties of the Trustees in general. The Associate Treasurer watches over the finances of Mathematical Reviews and over the administration of salary policy up to department head.

Applications

An Associate Treasurer is appointed by the Council upon recommendation of the Executive Committee and Board of Trustees. Applications, consisting of a CV and a letter expressing interest and relevant background, should be sent to:

AT Search Committee c/o Sandy Golden Office of AMS Secretary Department of Mathematics University of Tennessee, Knoxville, TN 37996-1330

email: [email protected]

Applications received by 15 February 2009 will be assured full consideration.

The American Mathematical Society is an Equal Opportunity Employer. www.ams.org 2008 Election Results

In the elections of 2008 the Society elected a vice presi- Editorial Boards Committee dent, a trustee, five members at large of the Council, three Elected as new members of the Editorial Boards Commit- members of the Nominating Committee, and two members tee are of the Editorial Boards Committee. Michael T. Lacey from the Georgia Institute of Tech- nology Vice President Michael F. Singer from the North Carolina State Elected as the new vice president is Frank Morgan University from Williams College in Williamstown, MA. Term is three Terms are three years (1 February 2009—31 January years (1 February 2009—31 January 2012). 2012). Trustee Elected as trustee is Ronald J. Stern from the University Proposal for a Fellows Program of the AMS of California, Irvine. Term is five years (1 February 2009— The proposal was NOT approved. 31 January 2014).

Members at Large of the Council Elected as new members at large of the Council are Aaron Bertram from the University of Utah William A. Massey from Princeton University Panagiotis E. Souganidis from the University of Chicago Michelle L. Wachs from the University of Miami David G. Wright from Washington University in St. Louis Terms are three years (1 February 2009—31 January 2012).

Nominating Committee Elected as new members of the Nominating Committee are Irene Fonseca from Carnegie Mellon University Sheldon H. Katz from the University of Illinois, Urbana Ellen E. Kirkman from Wake Forest University Terms are three years (1 January 2009—31 December 2011).

304 Notices of the AMS Volume 56, Number 2 2009 AMS Election Nominations by Petition Vice President or Rules and Procedures Use separate copies of the form for each candidate for vice Member at Large president, member at large, or member of the Nominating One position of vice president and member of the Council and Editorial Boards Committees. ex officio for a term of three years is to be filled in the election of 2009. The Council intends to nominate at least two 1. To be considered, petitions must be addressed to candidates, among whom may be candidates nominated Robert J. Daverman, Secretary, American Mathemati- by petition as described in the rules and procedures. cal Society, 312 D Ayres Hall, University of Tennessee, Five positions of member at large of the Council for a Knoxville, TN 37996-1330 USA, and must arrive by term of three years are to be filled in the same election. 24 February 2009. The Council intends to nominate at least ten candidates, 2. The name of the candidate must be given as it appears among whom may be candidates nominated by petition in in the Combined Membership List (www.ams.org/cml). the manner described in the rules and procedures. If the name does not appear in the list, as in the case Petitions are presented to the Council, which, according of a new member or by error, it must be as it appears to Section 2 of Article VII of the bylaws, makes the nomi- in the mailing lists, for example on the mailing label of nations. The Council of 23 January 1979 stated the intent the Notices. If the name does not identify the candidate of the Council of nominating all persons on whose behalf uniquely, append the member code, which may be ob- there were valid petitions. Prior to presentation to the Council, petitions in sup- tained from the candidate’s mailing label or by the can- port of a candidate for the position of vice president or didate contacting the AMS headquarters in Providence of member at large of the Council must have at least fifty ([email protected]). valid signatures and must conform to several rules and 3. The petition for a single candidate may consist of sev- operational considerations, which are described below. eral sheets each bearing the statement of the petition, including the name of the position, and signatures. The name of the candidate must be exactly the same Editorial Boards Committee on all sheets. Two places on the Editorial Boards Committee will be filled 4. On the next page is a sample form for petitions. Peti- by election. There will be four continuing members of the tioners may make and use photocopies or reasonable Editorial Boards Committee. facsimiles. The President will name at least four candidates for 5. A signature is valid when it is clearly that of the mem- these two places, among whom may be candidates nominated by petition in the manner described in the rules and ber whose name and address is given in the left-hand procedures. column. The candidate’s assent and petitions bearing at least 100 6. The signature may be in the style chosen by the signer. valid signatures are required for a name to be placed on However, the printed name and address will be checked the ballot. In addition, several other rules and operational against the Combined Membership List and the mail- considerations, described below, should be followed. ing lists. No attempt will be made to match variants of names with the form of name in the CML. A name neither in the CML nor on the mailing lists is not that Nominating Committee of a member. (Example: The name Robert J. Daverman Three places on the Nominating Committee will be filled is that of a member. The name R. Daverman appears by election. There will be six continuing members of the not to be.) Nominating Committee. 7. When a petition meeting these various requirements The President will name at least six candidates for these three places, among whom may be candidates nominated appears, the secretary will ask the candidate to indicate by petition in the manner described in the rules and willingness to be included on the ballot. Petitioners can procedures. facilitate the procedure by accompanying the petitions The candidate’s assent and petitions bearing at least 100 with a signed statement from the candidate giving valid signatures are required for a name to be placed on consent. the ballot. In addition, several other rules and operational considerations, described below, should be followed.

February 2009 Notices of the AMS 305 From the AMS Secretary Nomination Petition for 2009 Election

The undersigned members of the American Mathematical Society propose the name of

as a candidate for the position of (check one): Vice President Member at Large of the Council Member of the Nominating Committee Member of the Editorial Boards Committee of the American Mathematical Society for a term beginning 1 February, 2010 Return petitions by 24 February 2009 to: Secretary, AMS, 312 D Ayres Hall, University of Tennessee, Knoxville, TN 37996-1330 USA Name and address (printed or typed)

Signature

306 Notices of the AMS Volume 56, Number 2 Mathematics Calendar

Please submit conference information for the Mathematics Calendar through the Mathematics Calendar submission form at http://www.ams.org/cgi-bin/mathcal-submit.pl. The most comprehensive and up-to-date Mathematics Calendar information is available on the AMS website at http://www.ams.org/mathcal/.

February 2009 and marketing (e.g., data- and stream-mining), and finance techniques and algorithms from CS&E are of growing importance. * 1–12 IX Winter Russian Diffiety School — on Geometry of Par- Information: For more information, see: http://www.siam.org/ tial Differential Equations and Secondary Calculus, Sanatorij meetings/cse09/. “Kostromskoj”, Kostroma, Russia. Description: The aim of the permanent Diffiety School is to intro- * 6–8 2nd Bluegrass Algebra Conference, University of Kentucky, duce undergraduate and Ph.D. students in mathematics and physics Lexington, Kentucky. as well as post-doctoral researchers in a recently emerged area of Description: The conference continues a well established tradition of mathematics and teoretical physics: Secondary Calculus. A diffiety Commutative Algebra and Algebraic Geometry meetings in the Mid- is a new geometrical object that properly formalizes the concept of west, among which we single out MAGC97 at the University of Notre the solution space of a given system of (nonlinear) PDEs, much as an Dame in 1997, BACH’2 at the University of Kentucky in 2003, the Lip- algebraic variety does with respect to solutions of a given system of man-Fest at Purdue University in 2004, MAGIC’05 at the University of algebraic equations. Secondary calculus is a natural diffiety analogue Notre Dame in 2005, the Purdue-UIC Workshop at Purdue University of the standard calculus on smooth manifolds, and as such leads to in 2006, and the Hartshorne’s 70th birthday conference at the Univer- a very rich general theory of nonlinear PDEs. It appears that it is this sity of Illinois at Chicago in 2008. In order to enhance the visibility of the only natural language of quantum physics, just as the standard mathematics among the diverse population of the University of Ken- calculus is for classical physics. tucky students, the conference will be preceded by a lecture aimed Information: http://school.diffiety.org/page3/page0/ at the undergraduate level. The lecture will be delivered by Professor page92/page92.html. David Cox (Amherst College). Speakers: David Cox, Amherst College, Lawrence Ein, University of March 2009 Illinois at Chicago, Steven Kleiman, Massachusetts Institute of Tech- * 2–6 SIAM Conference on Computational Science and Engineering nology, Andrew Kustin, University of South Carolina, Sonja Petrovic, (CSE09), Miami Hilton Downtown, Miami, Florida. University of Illinois at Chicago, Paul Roberts, University of Utah, Maria Description: Computational Science and Engineering (CS&E) is now Evelina Rossi, Université di Genova (Italy), Hal Schenck, University of Il- widely accepted, along with theory and experiment, as a crucial third linois at Urbana-Champaign, Javid Validashti, University of Kansas. mode of scientific investigation and engineering design. Aerospace, Support: Mathematicians at the peridoctoral stage (meaning those automotive, biological, chemical, semiconductor, and other indus- who are close to finishing the doctorate or have recently finished) that trial sectors now rely on simulation for technical decision support. attend the conference will be supported through funds made available For government agencies also, CS&E has become an essential support by the National Science Foundation via the Special Algebra Meetings in for decisions on resources, transportation, and defense. Finally, in the Midwest grant (NSF DMS-0753127). They are encouraged to apply many new areas such as medicine, the life sciences, management at the conference Website by January 31, 2009.

This section contains announcements of meetings and conferences in the mathematical sciences should be sent to the Editor of the Notices in of interest to some segment of the mathematical public, including ad care of the American Mathematical Society in Providence or electronically hoc, local, or regional meetings, and meetings and symposia devoted to [email protected] or [email protected]. to specialized topics, as well as announcements of regularly scheduled In order to allow participants to arrange their travel plans, organizers of meetings of national or international mathematical organizations. A meetings are urged to submit information for these listings early enough complete list of meetings of the Society can be found on the last page to allow them to appear in more than one issue of the Notices prior to of each issue. the meeting in question. To achieve this, listings should be received in An announcement will be published in the Notices if it contains a call Providence eight months prior to the scheduled date of the meeting. for papers and specifies the place, date, subject (when applicable), and The complete listing of the Mathematics Calendar will be published the speakers; a second announcement will be published only if there are only in the September issue of the Notices. The March, June/July, and changes or necessary additional information. Once an announcement December issues will include, along with new announcements, references has appeared, the event will be briefly noted in every third issue until to any previously announced meetings and conferences occurring it has been held and a reference will be given in parentheses to the month, year, and page of the issue in which the complete information within the twelve-month period following the month of those issues. appeared. Asterisks (*) mark those announcements containing new or New information about meetings and conferences that will occur later revised information. than the twelve-month period will be announced once in full and will In general, announcements of meetings and conferences carry only not be repeated until the date of the conference or meeting falls within the date, title of meeting, place of meeting, names of speakers (or the twelve-month period. sometimes a general statement on the program), deadlines for abstracts The Mathematics Calendar, as well as Meetings and Conferences of or contributed papers, and source of further information. If there is any the AMS, is now available electronically through the AMS website on application deadline with respect to participation in the meeting, this the World Wide Web. To access the AMS website, use the URL: http:// fact should be noted. All communications on meetings and conferences www.ams.org/.

February 2009 Notices of the AMS 307 Mathematics Calendar

Information: http://www.ms.uky.edu/~algebra_uky_09. are welcome. There is no registration fee. Travel funding is available * 7–11 The Spring Topology and Dynamics Conference and the Ulam for participants based in the U.S. Information: http://www.math.uiuc.edu/~laugesen/ Centennial Conference, University of Florida, Gainesville, Florida. imaha05/imaha05.html. Description: The Spring Topology and Dynamics Conference is in its 41st year and each year brings together researchers from diverse April 2009 areas of topology and dynamics. Stanislaw Ulam, one of the preemi- nent mathematical scientists of the 20th century, was a graduate * 17–18 2009 Barrett Lectures, University of Tennessee, Knoxville, research professor at the University of Florida and will turn 100 in Tennessee. spring, 2009. In light of Ulam’s many contributions to topology, dy- Description: The scientific program of the meeting will cover a se- namics, and related fields, we are joining the annual STDC with an lection of applications of stochastic analysis. Professor Richard Bass Ulam Centennial. proposes to lecture on potential theory and integro-differential equa- Information: http://www.math.ufl.edu/stdculam/. tions while Professor Ofer Zeitouni intends to speak on problems in the study of random walks in random media. The one-hour invited * 15–21 Spring School on Index Theory, Lie Groupoids and Bound- speakers have not yet specified their talks but are expected to speak ary Value Problems, University of Regensburg, Germany. on filtering, partial differential equations driven by Levy processes, Topics: Index theory for foliations. Around ellipticity of boundary random polynomials, and other topics related to stochastic analysis conditions. From analysis on non-compact manifolds to boundary and its applications. value problems on polyhedral domains. Index theory, bordism and Topics: Stochastic Analysis and its Applications. rho-invariants. Index theory and positive scalar curvature. Main Speakers (three lectures each): Richard Bass, University of Organizers: Bernd Ammann and Ulrich Bunke. Connecticut; Ofer Zeitouni, University of Minnesota and Weizmann Speakers: Moulay-Tahar Benameur, Metz, France; Gilles Carron, Institute. Nantes, France; Victor Nistor, Penn State Univ., USA; Paolo Piazzo, Invited Speakers (one lecture each): Amarjit Budhiraja, University Rome, Italy; Thomas Schick, Goettingen, Germany. of North Carolina; Dan Crisan, Imperial College; Christian Houdre, Register: Please register as soon as possible by sending an email to Georgia Tech; Davar Khoshnevisan, University of Utah; Wembo Li, us. We have reserved a number of hotel rooms for participants of the University of Delaware. spring school. However, on December 15th, 2008, we either have to Talks: There will be eight contributed talks (15 minutes each). If you cancel the reservation or make the reservation legally binding. There would like to give a talk, please send the title and abstract to: jx- is a small budget to support participants of the spring school. Please [email protected] by February 28, 2009. We will choose eight contact us until Dec. 12th, 2008, in case you want to apply for support contributing speakers from the abstracts received. for travel or accomodation; Bernd Ammann, Ulrich Bunke. Organizers: X. Chen, B. Rajput, J. Rosinski, J. Xiong. Information: http://www.mathematik.uni-regensburg.de/ Sponsor: The 2009 Barrett Lectures is sponsored by the National Sci- ammann/springschool/. ence Foundation, the Department of Mathematics, and the University * 20–22 Southern Regional Algebra Conference 2009, University of of Tennessee. South Alabama, Mobile, Alabama. Information/Registration/Funding: Will be available for the partial Description: The Southern Regional Algebra Conference 2009 will take support of participants. Graduate students and young researchers place at the University of South Alabama in Mobile. All participants are are particularly invited to apply for support. On-line registration will invited to present 25-minute talks. The first talks will be scheduled be available starting in February. You can also register by sending an for friday afternoon, beginning approximately at 1:30 PM. The confer- email to: [email protected]. ence will end by noon on Sunday. As usual, no financial support will * 19–25 Spring School on Variational Analysis and its Applications, be provided for the participants by the University of South Alabama. Paseky nad Jizerou, Czech Republic. Graduate students are strongly encouraged to participate. Main speakers: F. Bonnans, A. Daniilidis, A. L. Dontchev, A. Ioffe. Organizers: Jörg Feldvoss, Cornelius Pillen, Yorck Sommerhäuser. Organizing committee: Marian Fabian, Jaroslav Lukes, Jiri Outrata Information: http://www.southalabama.edu/mathstat/ (Czech Republic). personal_pages/pillen/conference.html. Language: English. * 20–23 Cincinnati Symposium on Probability Theory and Applica- Grants: Probably support for a limited number of students. tions 2009, University of Cincinnati, Cincinnati, Ohio. Deadlines: For reduced fee and support: January 15, 2009. Description: The meeting will start on Friday at 3 pm with a Taft Information: http://www.karlin.mff.cuni.cz/katedry/kma/ lecture by professor S.R.S. Varadhan on large deviations in a random ss/apr09/; email: [email protected]. environment. Other lectures will cover new advances in studying the * 23–25 Twelfth New Mexico Analysis Seminar, University of New structure of a stochastic process via a martingale approximation; con- Mexico, Albuquerque, New Mexico. nections to ergodic theory; limit theorems and applications in statis- Goal: The goal of the conference is to provide an opportunity for sci- tics, finance, and statistical inference for random processes which may entific exchange and cooperation among broadly defined analysts. exhibit strong or long-range dependence, nonlinearity, heavy tails and There is time allocated for shorter contributed talks. Priority will be other features; large-dimensional random matrices. A unique feature given to graduate and postdoctoral students and those in early stages of our symposium is a series of four talks by experts on forensic ge- of their careers. nomics, which will take place on Saturday, March 21, 2 pm-6 pm. Organizers: Cristina Pereyra, email: [email protected]; Tiziana Information: http://math.uc.edu/free-gauss/CSP.htm. Giorgi, email: [email protected]; Joseph Lakey, email: jlakey@ * 27 Illinois/Missouri Applied Harmonic Analysis Seminar, University nmsu.edu; Adam Sikora, email: [email protected]; Robert Smits, of Illinois, Urbana, Illinois. email: [email protected]. This seminar is organized every year by Description: This half-day meeting fosters research interactions analysts at New Mexico State University and The University of New among mathematicians, engineers, and physicists who develop and Mexico. apply techniques from harmonic analysis. Keynote Speaker: Loukas Grafakos, University of Missouri at Co- Theoretical topics of interest: Fourier analysis, wavelets, Gabor lumbia: Lectures on “Linear and Multilinear Singular Integral Opera- systems (time-frequency analysis), frames, Riesz bases, compressed tors”. sensing, approximation theory, X-ray type transforms. Invited Speakers: Arpad Benyi (Western Washington University), and Applications of interest: All kinds of signal and image analysis, pro- Diego Maldonado (Kansas State University). cessing and reconstruction, both analogue and digital. Sponsor: NSF. Speakers: John J. Benedetto, Gitta Kutyniok, and Emmanuel Information: http://www.math.unm.edu/conferences/ Candes. 12thAnalysis. Support: This conference is supported in part by the Institute for Mathematics and its Application (IMA) through its Participating In- stitution (PI) Program. PI members may use IMA/PI funds to support travel of their personnel to this conference. All interested researchers

308 Notices of the AMS Volume 56, Number 2 Mathematics Calendar

May 2009 Description: Ph.D. students in pure mathematics, applied mathematics, mathematical statistics, mathematics education, or history of * 25–29 Indam School on symmetry for elliptic PDEs (30 years after mathematics from the Nordic countries are invited to participate in a conjecture of De Giorgi and related problems), Istituto Nazionale a summer school in mathematics organized by the European Women di Alta Matematica, Universita’ di Roma La Sapienza, Rome, Italy. in Mathematics (EWM). The summer school is especially aimed at en- Description: The school is open to graduate students and young re- couraging female students and researchers in their early careers, but searchers. The courses will be offered by Professors Xavier Cabré, we also warmly welcome male students. Students outside the Nordic Manuel del Pino, Ermanno Lanconelli and Ovidiu Savin. A few semi- countries, post-docs or advanced undergraduates thinking of Ph.D. nars will be also presented. The school is organized by Alberto Farina studies are also invited to attend. The program of the meeting is broad and Enrico Valdinoci. and will be of interest for students working in different research areas. Information: http://www.mat.uniroma2.it/~valdinoc/ Mini-courses will give an introduction and an overview over three cho- scuola-indam.html. sen topics of general interest from different areas of mathematics. * 31–June 6 Spring School on Analysis: Function Spaces, Inequalities They will be aimed at all students with a general mathematical back- and Interpolation, Paseky nad Jizerou, Czech Republic. ground, yet come to touch questions of current research. Main speakers: Anders Björn, Fernando Cobos, Thierry Coulhon, Information: http://www.math.utu.fi/projects/ewm. Peter A. Hästó. * 22–27 First Conference “Application of Mathematics in Technical Langage: English. and Natural Sciences” (AMiTaNS’09), Resort of Sozopol, Bulgaria. Information: http://www.karlin.mff.cuni.cz/katedry/kma/ Description: Papers on all subjects of application of mathematics ss/jun09/. in mechanics, physics, biology, chemistry and different engineer- June 2009 ing fields are invited. We plan to have several special sessions. The conference will consist of a few plenary talks by invitation from the * 1–5 Fifth Summer School in Analysis and Applied Mathematics, Program Committee, 60 minutes each. In each special session there Department of Mathematics, Sapienza, Universita’ di Roma, Rome, will be a couple of key lectures 45 minutes each. The invited presen- Italy. tations in the special sessions will be 30 minutes long. All contrib- Description: The school is intended mainly for Ph.D. students and uted talks will be 20 minutes long. If necessary, parallel sessions will young researchers in analysis and applied mathematics. be organized. Aim: The aim of the school is to provide a smooth trip in two impor- Information: http://www.eac4amitans.org. tant areas of the Calculus of Variations: Minimal Surfaces and Dif- ferential Inclusions. G. Alberti will guide the audience to a quick but * 22–July 3 Automorphic forms and L-functions, computational as- detailed introduction to the most important prerequisites. pects, CRM, Montreal, Canada. Speakers: The three speakers will be G. Alberti, S. Hildebrandt, and Description: The purpose of the school is to bring together a number L. Szekelyhidi Jr. of experts who have been leaders in both the theoretical and more Information: http://www.mat.uniroma1.it/people/garroni/ computational aspects of the theory of automorphic forms and L-func- School2009.html. tions, who will offer introductory-level courses aimed at presenting graduate students and post-doctoral fellows with the state of the art * 8–11 The 2nd International Conference on Mathematical Model- in the subject and report on new advances which have not yet been ling and Computation and The 5th East Asia SIAM Conference, covered in a forum of this sort. Universiti Brunei Darussalam, Bandar Seri Begawan, Brunei. Information: http://www.dms.umontreal.ca/~sms/ Description: The conference shall provide a venue to exchange ideas index_e.shtml. in the mathematical modelling of biological and physical systems, financial mathematics, and areas such as integral and differential op- * 25–27 Current Geometry: The X Edition of the International Confer- erators and numerical methods, in promoting both established and ence on Problems and Trends of Contemporary Geometry, Palazzo newer national and international research relationships. Serra di Cassano, Via Monte di Dio, 80132 Naples, Italy. Information: http://mmc09.ubd.edu.bn/. Description: The power of synthesis of geometry, which led in the past to the formulation of “grand unification theories”, has got an * 15–July 3 Summer School and Conference in Geometric Represen- essential role nowadays, especially because of the growing fragmentation Theory and Extended Affine Lie Algebras, University of Ot- tation of knowledge due to scientific progress. In order to avoid a big tawa, Ottawa, Ontario, Canada. dispersion, geometers need a constant dialogue. Therefore, a stable Description: The summer school will consist of three mini-courses experience of personal meetings, apart from telematic interchanges, per week for two weeks. These courses will serve as an introduction to cannot be renounced. Current geometry was born to allow a periodic geometric representation theory, quantum groups and combinatorial update about actual progresses in geometry (and its applications) on representation theory (i.e., the theory of crystal bases), the structure the international scene. theory of extended affine Lie algebras and the representation theory Information: http://www.levi-civita.org/CG2009.html. of affine and toroidal Lie algebras. They will be aimed at the graduate student/postdoctoral fellow level. Following the summer school there July 2009 will be a one-week conference featuring speakers presenting recent * 6–10 2009 SIAM Annual Meeting (AN09), Sheraton Denver Hotel, developments in areas related to the material of the summer school. Denver, Colorado. The event is sponsored by the Fields Institute (Toronto). Description: SIAM’s Annual Meeting provides a broad view of the Information: http://www.fields.utoronto.ca/programs/ state of the art in applied mathematics, computational science, and scientific/08-09/geomrep/. their applications through invited presentation, prize lectures, mini- * 16–22 Sixth International Workshop on Optimal Codes and Related symposia, and contributed papers and posters. Topics: OC 2009, Varna, Bulgaria. Information: http://www.siam.org/meetings/an09/. Description: This workshop gathers researchers on optimal linear * 16–31 XII Diffiety School — on Geometry of Partial differential codes and related problems. Equations and Secondary Calculus, Santo Stefano del Sole, Avellino, Topics include: Optimal linear codes over finite fields and rings, Italy. bounds for codes, spherical codes and designs, covering problems Description: The aim of this permanent school is to introduce under- for linear and nonlinear codes, optimization problems for nonlinear graduate and Ph.D. students in mathematics and physics as well as codes, sets of points in finite geometries, combinatorial configura- post-doctoral researchers in a recently emerged area of mathematics tions and codes, optimality problems in cryptography, graph theory and theoretical physics: Secondary Calculus. A diffiety is a new geo- and codes, and related topics. metrical object that properly formalizes the concept of the solution Information: http://www.moi.math.bas.bg/oc2009/oc2009. space of a given system of (nonlinear) PDEs, much as an algebraic html. variety does with respect to solutions of a given system of algebraic * 22–27 3rd Nordic EWM Summer School for Ph.D. Students in Math- equations. Secondary calculus is a natural diffiety analogue of the ematics, University of Turku, Turku, Finland. standard calculus on smooth manifolds, and as such leads to a very

February 2009 Notices of the AMS 309 Mathematics Calendar

rich general theory of nonlinear PDEs. It appears that it is the only ning for these conferences, the major objective has been the devel- natural language of quantum physics, just as the standard calculus opment and encouragement of industrial, government, and academic is for classical physics. collaboration. The format of this conference continues to provide Information: http://school.diffiety.org/page3/page0/ a forum for industrial and government engineers and scientists to page93/page93.html. communicate their needs, objectives, and visions, to the broad mathematical community. In 2009 an all-electronic proceedings will be in- * 31–August 2 3rd Jairo Charris Seminar—Symmetries of differen- troduced providing a unique and convenient opportunity for the SIAM tial and difference equations, Universidad Sergio Arboleda, Bogotá, community to publish applications of and research in applied math- Colombia. ematics. The major themes continue to fit the important categories of Description: The Jairo Charris Seminar is an annual event organized Challenges, Frontiers, and Industrial Academic Collaborations. by the Sergio Arboleda University. It is dedicated to Jairo Antonio Information: http://www.siam.org/meetings/calendar. Charris Castañeda (1939-2003), who was one of the fathers of the php. Colombian mathematical research and former professor of our university. November 2009 Topics: Symmetries of differential and difference equations. Algebraic Southern Right Delta ( P ’09) Conference on the methods in differential and difference equations. Integrability, solv- * 29–December 4 Σ ∆ Teaching and Learning of Undergraduate Mathematics and Sta- ability and reducibility of differential and difference equations. tistics, Gordon’s Bay, Western Cape, South Africa. Information: http://www.usergioarboleda.edu.co/ Description: The seventh bi-annual Delta conference on the teaching matematicas/jairo_charris.htm. and learning of undergraduate mathematics and statistics (ΣP∆’09) August 2009 takes place in the picturesque beach town of Gordon’s Bay, close to Cape Town, South Africa. ΣP∆’09 forms part of the series of Delta * 3–14 Pan-American Advanced Studies Institute (PASI): In Commu- conferences, a southern hemisphere initiative. tative Algebra and its connections to Geometry, Olinda, Brazil. Information: http://www.delta2009.co.za/index_html. Description: The two week program is sponsored by a PASI grant from the Office of International Science & Engineering of the NSF. The pro- December 2009 gram will consist of six mini-courses on fundamental techniques in * 7–9 SIAM Conference on Analysis of Partial Differential Equations commutative algebra and related fields during the first week (school). (PD09), Hilton Miami Downtown, Miami, Florida. The second week will be devoted to a series of advanced research Description: This conference is organized by the SIAM Activity Group talks by recognized leaders in the area (international workshop). The (SIAG) on Analysis of Partial Differential Equations (SIAG/APDE). courses will bring junior researchers up-to-speed in the more special- Information: The website will be updated as additional information ized topics that will be the focus of the advanced lectures and will becomes available. http://www.siam.org/meetings/calen- contribute to the training of young researchers from the Americas. dar.php. Organizers: A. Corso, C. Huneke C. Polini, A. Simis, and B. Ulrich. School speakers: David Cox, Amherst College (USA), Juergen Herzog, University of Duiburg-Essen (Germany), Craig Huneke, University of Kansas (USA), Steven Kleiman, MIT (USA), Maria Evelina Rossi, Univer- sità di Genova (Italy), Bernd Ulrich, Purdue University (USA). Support: Mathematicians from the Americas at the peridoctoral stage (meaning those who are close to finishing the doctorate or have recently finished) that attend the school will be supported through funds made available by the National Science Foundation via the PASI program. They are encouraged to apply at the conference web site by March 31, 2009. Information: http://www.ms.uky.edu/~pasi2009. * 17–21 International Conference on Complex Analysis and Related Topics, University of Turku, Turku, Finland. Description: This conference is the 12th one in the series of Roma- nian-Finnish Seminars on topics related to mathematical analysis. The conference is open to all nationalities. Information: http://www.math.utu.fi/romfin2009/. September 2009 * 2–4 Workshop in nonlinear elliptic PDEs, Université Libre de Brux- elles, Brussels, Belgium. Description: The workshop is organized on the occasion of the 65th birthday of Jean-Pierre Gossez. Speakers: The following lecturers have confirmed their participation: Henri Berestycki (Paris), Philippe Clément (Delft), Djairo G. de Figueiredo (Campinas), François de Thélin (Toulouse), Pavel Drabek (Pilsen), Ivar Ekeland (Vancouver), Jesús Hernández (Madrid), Bernd Kawohl (Köln), Pierre-Louis Lions (Paris), Jean Mawhin (Louvain-la- Neuve), Petru Mironescu (Lyon), Mark Peletier (Eindhoven), Frédéric Robert (Nice), Bernhard Ruf (Milano), Michael Struwe (Zurich), Charles Stuart (Lausanne), Juan Luis Vazquez (Madrid). Information: http://wnpde09.ulb.ac.be/. October 2009 * 9–11 SIAM Conference on Mathematics for Industry: Challenges and Frontiers (MI09), Hilton San Francisco Financial District, San Francisco, California. Description: The SIAM conferences on Mathematics for Industry focus attention on the many and varied opportunities to promote applications of mathematics to industrial problems. From the start of plan-

310 Notices of the AMS Volume 56, Number 2 New Publications Oﬀered by the AMS To subscribe to email notiﬁcation of new AMS publications, please go to http://www.ams.org/bookstore-email.

Algebra and Algebraic Geometric positivity in the cohomology of homogeneous spaces and generalized Schubert calculus; G. Farkas, The global geometry of Geometry the moduli space of curves; M. Gross, The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations; S. Grushevsky, Geometry of Ag and its compactifications; D. Huybrechts, The global Torelli theorem: classical, derived, twisted; A. Kresch, On the Algebraic Geometry geometry of Deligne-Mumford stacks; A. Langer, Moduli spaces of sheaves and principal G-bundles; Y.-P. Lee, Notes on axiomatic Seattle 2005 Gromov-Witten theory and applications; A. Okounkov and R. Pandharipande, Gromov-Witten theory, Hurwitz numbers, and D. Abramovich, Brown matrix models; P. Seidel, Symplectic homology as Hochschild University, Providence, RI, homology; B. Toën, Higher and derived stacks: a global overview; A. Bertram, University of Utah, Part II: M. A. A. De Cataldo and L. Migliorini, Hodge-theoretic Salt Lake City, UT, , aspects of the decomposition theorem; L. Ein and M. Musta¸t˘a, L. Katzarkov Jet schemes and singularities; H. Gangl, A. B. Goncharov, University of Miami, Coral Gables, and A. Levin, Multiple polylogarithms, polygons, trees and FL, R. Pandharipande, Princeton algebraic cycles; D. Kaledin, Geometry and topology of symplectic ∗ University, NJ, and M. Thaddeus, resolutions; S. Kaliman, Actions of C and C+ on affine algebraic Columbia University, New York, varieties; Y. Kawamata, Derived categories and birational geometry; NY, Editors K. S. Kedlaya, p-adic cohomology; S. A. Kovács, Subvarieties of moduli stacks of canonically polarized varieties: generalizations of Shafarevich’s conjecture; S. J. Kovács, Young person’s guide to The 2005 AMS Summer Institute on Algebraic Geometry in Seattle moduli of higher dimensional varieties; F. Loeser, Seattle lectures was an enormous event. With over 500 participants, including on motivic integration; M. Manetti, Differential graded Lie algebras many of the world’s leading experts, it was perhaps the largest and formal deformation theory; M. C. Olsson, On Faltings’ method conference on algebraic geometry ever held. These two proceedings of almost étale extensions; B. Hassett and Y. Tschinkel, Weak volumes present research and expository papers by some of the approximation for hypersurfaces of low degree; J. Włodarczyk, most outstanding speakers at the meeting, vividly conveying the Simple constructive weak factorization. grandeur and vigor of the subject. Proceedings of Symposia in Pure Mathematics, Volume 80 The most exciting topics in current algebraic geometry research receive very ample treatment. For instance, there is enlightening Part 1: March 2009, approximately 478 pages, Hardcover, ISBN: information on many of the latest technical tools, from jet schemes 978-0-8218-4702-2, LC 2008044494, 2000 Mathematics Subject and derived categories to algebraic stacks. Numerous papers Classification: 14-XX; 14-06, 11Gxx, 18E30, 32Cxx, 32Gxx, 32Sxx, delve into the geometry of various moduli spaces, including those 53Dxx, 55U35, Order code PSPUM/80.1 of stable curves, stable maps, coherent sheaves, and abelian Part 2: March 2009, approximately 520 pages, Hardcover, ISBN: varieties. Other papers discuss the recent dramatic advances in 978-0-8218-4703-9, LC 2008044494, 2000 Mathematics Subject higher-dimensional birational geometry, while still others trace the Classification: 14-XX; 14-06, 11Gxx, 18E30, 32Cxx, 32Gxx, 32Sxx, influence of quantum field theory on algebraic geometry via mirror 53Dxx, 55U35, Order code PSPUM/80.2 symmetry, Gromov–Witten invariants, and symplectic geometry. Set: March 2009, approximately 998 pages, Hardcover, ISBN: The proceedings of earlier algebraic geometry AMS Institutes, held 978-0-8218-4057-3, LC 2008044494, 2000 Mathematics Subject at Woods Hole, Arcata, Bowdoin, and Santa Cruz, have become classics. The present volumes promise to be equally influential. Classification: 14-XX; 14-06, 11Gxx, 18E30, 32Cxx, 32Gxx, 32Sxx, They present the state of the art in algebraic geometry in papers 53Dxx, 55U35, AMS members US$139, List US$174, Order code that will have broad interest and enduring value. PSPUM/80 Contents: Part I: T. Bridgeland, Spaces of stability conditions; J. Bryan and T. Graber, The crepant resolution conjecture; R. L. Cohen and I. Madsen, Surfaces in a background space and the homology of mapping class groups; I. Coskun and R. Vakil,

February 2009 Notices of the AMS 311 New Publications Oﬀered by the AMS

“Abstract” Tensor-product interpolation; The Boolean algebra of projections; The Newton paradigm for interpolation; The Lagrange paradigm Homomorphisms for interpolation; Interpolation by translates of a single function; of Split Kac-Moody Positive definite functions; Strictly positive definite functions; Completely monotone functions; The Schoenberg interpolation Groups theorem; The Micchelli interpolation theorem; Positive definite Pierre-Emmanuel Caprace, functions on spheres; Approximation by positive definite functions; Approximate reconstruction of functions and tomography; Université Libre de Bruxelles, Approximation by convolution; The good kernels; Ridge functions; Belgium Ridge function approximation via convolutions; Density of ridge functions; Artificial neural networks; Chebyshev centers; Optimal Contents: The objects: Kac-Moody groups, reconstruction of functions; Algorithmic orthogonal projections; root data and Tits buildings; Basic tools Cardinal B-splines and the sinc function; The Golomb-Weinberger from geometric group theory; Kac-Moody groups and algebraic theory; Hilbert function spaces and reproducing kernels; groups; Isomorphisms of Kac-Moody groups: an overview; Spherical thin-plate splines; Box splines; Wavelets, I; Wavelets, II; Isomorphisms of Kac-Moody groups in characteristic zero; Quasi-interpolation; Bibliography; Index; Index of symbols. Isomorphisms of Kac-Moody groups in positive characteristic; Homomorphisms of Kac-Moody groups to algebraic groups; Unitary Graduate Studies in Mathematics, Volume 101 forms of Kac-Moody groups; Bibliography; Index. March 2009, 359 pages, Hardcover, ISBN: 978-0-8218-4798-5, LC Memoirs of the American Mathematical Society, Volume 198, 2008047417, 2000 Mathematics Subject Classification: 41-01, AMS Number 924 members US$55, List US$69, Order code GSM/101 March 2009, 84 pages, Softcover, ISBN: 978-0-8218-4258-4, LC 2008047593, 2000 Mathematics Subject Classification: 17B40, 20E36, 20E42, 20G15, 22E65, 51E24, Individual member Communicating US$39, List US$65, Institutional member US$52, Order code Mathematics MEMO/198/924 Timothy Y. Chow, Center for Communications Research, Princeton, NJ, and Daniel C. A Course in Isaksen, Wayne State University, Approximation Detroit, MI, Editors This volume contains the proceedings Theory of a conference held in July, 2007 at the Ward Cheney, University of University of Minnesota, Duluth, in honor Texas at Austin, TX, and Will of Joseph A. Gallian’s 65th birthday and the 30th anniversary of the Light Duluth Research Experience for Undergraduates. In keeping with Gallian’s extraordinary expository ability and This textbook is designed for graduate broad mathematical interests, the articles in this volume span a students in mathematics, physics, wide variety of mathematical topics, including algebraic topology, engineering, and computer science. combinatorics, design theory, forcing, game theory, geometry, Its purpose is to guide the reader in graph theory, group theory, optimization, and probability. exploring contemporary approximation theory. The emphasis is on Some of the papers are purely expository while others are multi-variable approximation theory, i.e., the approximation of research articles. The papers are intended to be accessible to a functions in several variables, as opposed to the classical theory of general mathematics audience, including first-year or second-year functions in one variable. graduate students. This volume should be especially useful for Most of the topics in the book, heretofore accessible only through mathematicians seeking a new research area, as well as those research papers, are treated here from the basics to the currently looking to enrich themselves and their research programs by active research, often motivated by practical problems arising learning about problems and techniques used in other areas of in diverse applications such as science, engineering, geophysics, mathematics. and business and economics. Among these topics are projections, This item will also be of interest to those working in discrete interpolation paradigms, positive definite functions, interpolation mathematics and combinatorics and geometry and topology. theorems of Schoenberg and Micchelli, tomography, artificial neural networks, wavelets, thin-plate splines, box splines, ridge functions, Contents: S. S. Adams, A journey of discovery: Orthogonal and convolutions. matrices and wireless communications; J. Beam, Probabilistic expectations on unstructured spaces; T. Y. Chow, A beginner’s An important and valuable feature of the book is the bibliography of guide to forcing; E. Constantin, Higher order necessary conditions almost 600 items directing the reader to important books and in smooth constrained optimization; D. Dunham, Hamiltonian research papers. There are 438 problems and exercises scattered paths and hyperbolic patterns; J. S. Foisy and L. D. Ludwig, When through the book allowing the student reader to get a better graph theory meets knot theory; J. Friedman and C. Parker, Can an understanding of the subject. asymmetric power structure always be achieved?; S. G. Hartke Contents: Introductory discussion of interpolation; Linear and A. J. Radcliffe, McKay’s canonical graph labeling algorithm; interpolation operators; Optimization of the Lagrange operator; P. Hersh and R. Kleinberg, A multiplicative deformation of the Multivariate polynomials; Moving the nodes; Projections; Möbius function for the poset of partitions of a multiset; A. Higgins,

312 Notices of the AMS Volume 56, Number 2 New Publications Oﬀered by the AMS

Communicating, mathematics, communicating mathematics–Joe families in commutative rings; S. López-Permouth and S. Szabo, Gallian style; D. Housman, Fair allocation methods for coalition Matrix representations of skew polynomial rings with semisimple games; D. C. Isaksen, Sums-of-squares formulas; K. S. Kedlaya, coefficient rings; P. Pappas, Topological representations of von Product-free subsets of groups, then and now; K. S. Kedlaya and Neumann regular algebras; E. R. Puczylowski, A unified approach X. Shao, Generalizations of product-free subsets; D. W. Morris, to some results on one-sided ideals and matrix rings of associative What is a supergrid subgroup?; D. P. Moulton, Averaging points rings; J. Trlifaj and D. Pospıšil, Tilting and cotilting classes over two at a time; M. M. Patnaik, Vertex algebras as twisted bialgebras: Gorenstein rings; R. Wiegand and S. Wiegand, Semigroups of On a theorem of Borcherds. modules: A survey; R. Wisbauer, Generators in module and commodule categories. Contemporary Mathematics, Volume 479 Contemporary Mathematics, Volume 480 March 2009, 238 pages, Softcover, ISBN: 978-0-8218-4345-1, LC 2008036377, 2000 Mathematics Subject Classification: 00B20, March 2009, 361 pages, Softcover, ISBN: 978-0-8218-4370-3, LC 00B30, AMS members US$63, List US$79, Order code CONM/479 2008039856, 2000 Mathematics Subject Classification: 13-XX, 16-XX, 18-XX, AMS members US$79, List US$99, Order code CONM/480 Rings, Modules and Representations Algebra Nguyen Viet Dung, Ohio A Graduate Course University, Zanesville, OH, Franco Guerriero, Ohio University, I. Martin Isaacs, University of Lancaster, OH, Lakhdar Wisconsin, Madison, WI Hammoudi, Ohio University, This book, based on a first-year graduate Chillicothe, OH, and Pramod course the author taught at the University Kanwar, Ohio University, of Wisconsin, contains more than enough Zanesville, OH, Editors material for a two-semester graduate-level abstract algebra course, including groups, This volume originated from talks given at the International rings and modules, fields and Galois Conference on Rings and Things held in June, 2007 at Ohio theory, an introduction to algebraic number theory, and the University–Zanesville. rudiments of algebraic geometry. In addition, there are some The papers in this volume contain the latest results in current more specialized topics not usually covered in such a course. active research areas in the theory of rings and modules, including These include transfer and character theory of finite groups, noncommutative and commutative ring theory, module theory, modules over artinian rings, modules over Dedekind domains, and representation theory, and coding theory. In particular, papers transcendental field extensions. in this volume deal with topics such as decomposition theory of This book could be used for self study as well as for a course modules, injectivity and generalizations, tilting theory, rings text, and so full details of almost all proofs are included, with and modules with chain conditions, Leavitt path algebras, nothing being relegated to the chapter-end problems. There are, representations of finite dimensional algebras, and codes over rings. however, hundreds of problems, many being far from trivial. While most of these papers are original research articles, some are The book attempts to capture some of the informality of the expository surveys. classroom, as well as the excitement the author felt when taking the This book is suitable for graduate students and researchers corresponding course as a student. interested in noncommutative ring and module theory, Contents: Part One, Noncommutative Algebra: Definitions and representation theory, and applications. examples of groups; Subgroups and cosets; Homomorphisms; Contents: D. D. Anderson and V. Camillo, Subgroups of direct Group actions; The Sylow theorems and p-groups; Permutation products of groups, ideals and subrings of direct products groups; New groups from old; Solvable and nilpotent groups; of rings, and Goursat’s lemma; G. F. Birkenmeier, J. K. Park, Transfer; Operator groups and unique decompositions; Module and S. T. Rizvi, An example of Osofsky and essential overrings; theory without rings; Rings, ideals, and modules; Simple modules W. D. Burgess and R. Raphael, On commutative clean rings and and primitive rings; Artinian rings and projective modules; pm rings; E. S. Campos and P. F. Smith, Modules satisfying the An introduction to character theory; Part Two, Commutative ascending chain condition on submodules with bounded uniform Algebra: Polynomial rings, PIDs, and UFDs; Field extensions; Galois dimension; J. Dauns, Relative purity, flatness, and injectivity; H. Q. theory; Separability and inseparability; Cyclotomy and geometric Dinh, Repeated-root constacyclic codes of prime power length; constructions; Finite fields; Roots, radicals, and real numbers; A. N. Duca, The socle series of indecomposable injective modules Norms, traces, and discriminants; Transcendental extensions; The over a principal left and right ideal domain; N. Er, Some remarks Artin-Schreier theorem; Ideal theory; Noetherian rings; Integrality; on a question of Faith; A. Facchini, Subdirect representations of Dedekind domains; Algebraic sets and the nullstellensatz; Index. categories of modules; J. L. Gómez Pardo and P. A. Guil Asensio, Graduate Studies in Mathematics, Volume 100 Fitting’s lemma for modules with well-behaved clones; K. R. January 2009, 516 pages, Hardcover, ISBN: 978-0-8218-4799-2, LC Goodearl, Leavitt path algebras and direct limits; D. Herbera, Simple modules over small rings; B. Huisgen-Zimmermann,A 2008047416, 2000 Mathematics Subject Classification: 00A05; 12- hierarchy of parametrizing varieties for representations; D. V. 01, 13-01, 16-01, 20-01, AMS members US$63, List US$79, Order Huynh, D. D. Tai, and L. V. An, On the CS condition and rings with code GSM/100 chain conditions; S. K. Jain, T. Y. Lam, and A. Leroy, Ore extensions and V -domains; T. Y. Lam and M. L. Reyes, Oka and Ako ideal

February 2009 Notices of the AMS 313 New Publications Offered by the AMS Analysis Function Theory: Interpolation and Corona Problems Introduction to Eric T. Sawyer, McMaster Fourier Analysis and University, Hamilton, ON, Canada Wavelets These lecture notes take the reader from Lennart Carleson’s first deep results on Mark A. Pinsky, Northwestern interpolation and corona problems in the University, Evanston, IL unit disk to modern analogues in the disk and ball. The emphasis is on introducing This book provides a concrete the diverse array of techniques needed to attack these problems introduction to a number of topics in rather than producing an encyclopedic summary of achievements. harmonic analysis, accessible at the early Techniques from classical analysis and operator theory include graduate level or, in some cases, at an duality, Blaschke product constructions, purely Hilbert space upper undergraduate level. Necessary arguments, bounded mean oscillation, best approximation, prerequisites to using the text are rudiments of the Lebesgue boundedness of the Beurling transform, estimates on solutions to measure and integration on the real line. It begins with a thorough the ∂¯equation, the Koszul complex, use of trees, the complete Pick treatment of Fourier series on the circle and their applications property, and the Toeplitz corona theorem. An extensive appendix to approximation theory, probability, and plane geometry (the on background material in functional analysis and function theory isoperimetric theorem). Frequently, more than one proof is offered on the disk is included for the reader’s convenience. for a given theorem to illustrate the multiplicity of approaches. Titles in this series are co-published with The Fields Institute for The second chapter treats the Fourier transform on Euclidean Research in Mathematical Sciences (Toronto, Ontario, Canada). spaces, especially the author’s results in the three-dimensional piecewise smooth case, which is distinct from the classical Contents: Preliminaries; The interpolation problem; The corona Gibbs–Wilbraham phenomenon of one-dimensional Fourier problem; Toeplitz and Hankel operators; Hilbert function spaces analysis. The Poisson summation formula treated in Chapter 3 and Nevanlinna-Pick kernels; Carleson measures for the Hardy- provides an elegant connection between Fourier series on the circle Sobolev spaces; Functional analysis; Weak derivatives and Sobolev and Fourier transforms on the real line, culminating in Landau’s spaces; Function theory on the disk; Spectral theory for normal asymptotic formulas for lattice points on a large sphere. operators; Bibliography; Index. Much of modern harmonic analysis is concerned with the behavior Fields Institute Monographs, Volume 25 p n of various linear operators on the Lebesgue spaces L (R ). Chapter February 2009, 203 pages, Hardcover, ISBN: 978-0-8218-4734-3, 4 gives a gentle introduction to these results, using the Riesz–Thorin LC 2008047418, 2000 Mathematics Subject Classification: 30-02, theorem and the Marcinkiewicz interpolation formula. One of the 30H05, 32A35; 32A38, 42B30, 46J10, AMS members US$52, List long-time users of Fourier analysis is probability theory. In Chapter US$65, Order code FIM/25 5 the central limit theorem, iterated log theorem, and Berry–Esseen theorems are developed using the suitable Fourier-analytic tools. The final chapter furnishes a gentle introduction to wavelet theory, depending only on the L2 theory of the Fourier transform (the Differential Equations Plancherel theorem). The basic notions of scale and location parameters demonstrate the flexibility of the wavelet approach to harmonic analysis. The text contains numerous examples and more than 200 exercises, Multi-Pulse Evolution each located in close proximity to the related theoretical material. and Space-Time Chaos Contents: Fourier series on the circle; Fourier transforms on the in Dissipative Systems line and space; Fourier analysis in Lp spaces; Poisson summation formula and multiple Fourier series; Applications to probability Sergey Zelik, University of theory; Introduction to wavelets; References; Notations; Index. Surrey, Guildford, United Graduate Studies in Mathematics, Volume 102 Kingdom, and Alexander February 2009, 376 pages, Hardcover, ISBN: 978-0-8218-4797-8, Mielke, Weierstrass Institut LC 2008047419, 2000 Mathematics Subject Classification: 42-02; für Angewandte Analysis und 42C40, AMS members US$55, List US$69, Order code GSM/102 Stochastik, Berlin, Germany

This item will also be of interest to those working in probability. Contents: Introduction; Assumptions and preliminaries; Weighted Sobolev spaces and regularity of solutions; The multi-pulse manifold: general structure; The multi-pulse manifold: projectors and tangent spaces; The multi-pulse manifold: differential equations and the cut off procedure; Slow evolution of multi-pulse profiles: linear case; Slow evolution of multi-pulse structures: center manifold reduction; Hyperbolicity and stability; Multi-pulse

314 Notices of the AMS Volume 56, Number 2 New Publications Offered by the AMS evolution equations: asymptotic expansions; An application: …an excellent series transferring contemporary mathe- spatio-temporal chaos in periodically perturbed Swift-Hohenberg matical research in a delightful and exact manner to both equation; Bibliography; Nomenclature. non-mathematicians and mathematicians. Memoirs of the American Mathematical Society, Volume 198, The mixture of hot topics and profiles of outstanding mathemati- Number 925 cians proves a good choice. …Hopefully it will reach teachers and educators in order to make mathematics more visible and perhaps March 2009, 97 pages, Softcover, ISBN: 978-0-8218-4264-5, LC a bit more understandable to the general public. 2008047916, 2000 Mathematics Subject Classification: 35Q30, —Zentralblatt MATH 37L30, Individual member US$39, List US$65, Institutional mem- Contents: Introduction; A new twist in knot theory; Error-term ber US$52, Order code MEMO/198/925 roulette and the Sato-Tate conjecture; The fifty-one percent solution; Dominos, anyone?; Not seeing is believing; Getting with the (Mori) program; The book that time couldn’t erase; Charting a 248-dimensional world; Compressed sensing makes every pixel count. General and Interdisciplinary What’s Happening in the Mathematical Sciences, Volume 7 February 2009, 127 pages, Softcover, ISBN: 978-0-8218-4478-6, 2000 Mathematics Subject Classification: 00A06, AMS members What’s Happening US$15.95, List US$19.95, Order code HAPPENING/7 in the Mathematical Sciences Dana Mackenzie Circle in a Box Sam Vandervelde, St. Lawrence Since 1993, the AMS has been publishing University, Canton, NY What’s Happening in the Mathematical Sciences, a series of lively and highly Math circles provide a setting in which readable accounts of the latest mathematicians work with secondary developments in mathematics. This school students who are interested in seventh volume describes some genuine mathematics. This form of outreach, surprises, such as the recent discovery that coin tosses are which has existed for decades in Russia, inherently unfair; a mathematical theory of invisibility that was Bulgaria, and other countries, is now soon followed by the creation of a prototype “invisibility cloak”; rapidly spreading across the United States and an ultra-efficient approach to image sensing that led to the as well. The first part of this book offers development of a single-pixel camera. helpful advice on all aspects of math circle operations, culled from The past few years have also seen deep results on some classical conversations with over a dozen directors of successful math mathematics problems. For example, this volume describes a circles. Topics include creative means for getting the word out proof of the Sato–Tate Conjecture in number theory and a major to students, sound principles for selecting effective speakers, advance in the Minimal Model Program of algebraic geometry. The guidelines for securing financial support, and tips for designing an computation of the character table of the exceptional Lie group E8 exciting math circle session. The purpose of this discussion is brings “the most beautiful structure in mathematics” to public to enable math circle coordinators to establish a thriving group attention, and proves that human persistence is just as important as in which students can experience the delight of mathematical gigabytes of RAM. The amazing story of the Archimedes Palimpsest investigation. The second part of the book outlines ten independent shows how the modern tools of high-energy physics uncovered the math circle sessions, covering a variety of topics and difficulty centuries-old secrets of the mathematical writings of Archimedes. levels. Each chapter contains detailed presentation notes along Dana Mackenzie, a science writer specializing in mathematics, with a useful collection of problems and solutions. This book will makes each of these topics accessible to all readers, with a style that be an indispensable resource for any individual involved with a is friendly and at the same time attentive to the nuances that make math circle or anyone who would like to see one begin in his or her mathematics fascinating. Anyone with an interest in mathematics, community. from high school teachers and college students to engineers and Sam Vandervelde teaches at St. Lawrence University. He launched computer scientists, will find something of interest here. The the Stanford Math Circle and also writes and coordinates the stories are well told and the mathematics is compelling. Mandelbrot Competition, a math contest for high schools. Praise for Earlier Volumes: Titles in this series are co-published with the Mathematical Sciences One can say without overstatement that the standards in these Research Institute (MSRI). volumes are very high indeed. Contents: Oversight: Molding a math circle; Supporting a math The articles are very well written, and usually include quotes from circle; Sustaining a math circle; Leading a math circle; Presentations: the mathematicians who were involved in the work in question, The game of Criss-Cross; Double time; King chickens; Into the giving the whole thing a more “human” feel. This book offers unknown; Sneaky segments; Heads or tails; Circling the square; professionals a way to keep abreast of what’s going on in the field Making change; Square dance; Reflection in a circle; Appendices: and also gives us a way to share with our students and colleagues Sample documents; Warm-ups; Sample grant proposal; Sample some of the excitement of doing mathematics. Don’t miss it. grant report; Acknowledgments. —MAA Online MSRI Mathematical Circles Library, Volume 2

February 2009 Notices of the AMS 315 New Publications Oﬀered by the AMS

February 2009, 217 pages, Softcover, ISBN: 978-0-8218-4752-7, Index Theory, Eta 2000 Mathematics Subject Classiﬁcation: 97D50; 97U40, 97A20, AMS members US$31, List US$39, Order code MCL/2 Forms, and Deligne Cohomology Ulrich Bunke, Universität Geometry and Topology Regensburg, Germany

Contents: Introduction; Index theory for families with corners; Analytic obstruction Applications of Knot theory; Deligne cohomology valued index Theory theory; Bibliography; Index. Dorothy Buck, Imperial College Memoirs of the American Mathematical Society, Volume 198, Number 928 London, England, and Erica Flapan, Pomona College, March 2009, 120 pages, Softcover, ISBN: 978-0-8218-4284- Claremont, CA, Editors 3, LC 2008047669, 2000 Mathematics Subject Classification: 58J28, 55S35, Individual member US$40, List US$67, Institutional Over the past 20–30 years, knot theory member US$54, Order code MEMO/198/928 has rekindled its historic ties with biology, chemistry, and physics as a means of creating more sophisticated descriptions Mathematical Physics of the entanglements and properties of natural phenomena—from strings to organic compounds to DNA. This volume is based on the 2008 AMS Short Course, Applications of Knot Theory. The aim of the Short Course and this volume, while Canonical Wick not covering all aspects of applied knot theory, is to provide the reader with a mathematical appetizer, in order to stimulate the Rotations in mathematical appetite for further study of this exciting field. 3-Dimensional Gravity No prior knowledge of topology, biology, chemistry, or physics Riccardo Benedetti, Università is assumed. In particular, the first three chapters of this volume di Pisa, Italy, and Francesco introduce the reader to knot theory (by Colin Adams), topological chirality and molecular symmetry (by Erica Flapan), and DNA Bonsante, Università degli Studi topology (by Dorothy Buck). The second half of this volume is di Pavia, Italy focused on three particular applications of knot theory. Louis Kauffman discusses applications of knot theory to physics, Nadrian Contents: General view on themes and Seeman discusses how topology is used in DNA nanotechnology, contents; Geometry models; Flat globally and Jonathan Simon discusses the statistical and energetic hyperbolic spacetimes; Flat Lorentzian vs hyperbolic geometry; Flat properties of knots and their relation to molecular biology. vs de Sitter Lorentzian geometry; Flat vs AdS Lorentzian geometry; QD-spacetimes; Complements; Bibliography; Index. This item will also be of interest to those working in applications. Memoirs of the American Mathematical Society, Volume 198, Contents: C. Adams, A brief introduction to knot theory from Number 926 the physical point of view; E. Flapan, Topological chirality and symmetries of non-rigid molecules; D. Buck, DNA topology; March 2009, 164 pages, Softcover, ISBN: 978-0-8218-4281-2, L. H. Kauffman, Knots and physics; N. C. Seeman, Synthetic LC 2008047655, 2000 Mathematics Subject Classification: 53C50, single-stranded DNA topology; J. Simon, Long tangled filaments. 57M50, Individual member US$43, List US$72, Institutional Proceedings of Symposia in Applied Mathematics, Volume 66 member US$58, Order code MEMO/198/926 March 2009, approximately 187 pages, Hardcover, ISBN: 978-0-8218- 4466-3, LC 2008044393, 2000 Mathematics Subject Classification: 53A04, 57M25, 57M27, 81T45, 82D60, 92C40, 92E10, AMS members US$39, List US$49, Order code PSAPM/66

316 Notices of the AMS Volume 56, Number 2 New AMS-Distributed Publications

Number Theory 60G50, 60J55, Individual member US$37, List US$62, Institutional member US$50, Order code MEMO/198/929

Class Field Theory Brownian Brownian Emil Artin, and John Tate, Motion-I University of Texas at Austin, TX N. Chernov, University of This classic book, originally published Alabama, Birmingham, AL, and in 1968, is based on notes of a year-long D. Dolgopyat, University of seminar the authors ran at Princeton Maryland, College Park, MD University. The primary goal of the book was to give a rather complete presentation Contents: Introduction; Statement of of algebraic aspects of global class field results; Plan of the proofs; Standard pairs theory, and the authors accomplished this and equidistribution; Regularity of the goal spectacularly: for more than 40 years diffusion matrix; Moment estimates; Fast since its first publication, the book has served as an ultimate source slow particle; Small large particle; Open problems; Appendix A. for many generations of mathematicians. Statistical properties of dispersing billiards; Appendix B. Growth and distortion properties of dispersing billiards; Appendix C. In this revised edition, two mathematical additions complementing Distortion bounds for two particle system; Bibliography; Index. the exposition in the original text are made. The new edition also contains several new footnotes, additional references, and Memoirs of the American Mathematical Society, Volume 198, historical comments. Number 927 Contents: Preliminaries; The first fundamental inequality; Second March 2009, 193 pages, Softcover, ISBN: 978-0-8218-4282-9, fundamental inequality; Reciprocity law; The existence theorem; LC 2008047662, 2000 Mathematics Subject Classification: 37D50; Connected component of idèle classes; The Grunwald–Wang 34C29, 60F17, Individual member US$47, List US$78, Institutional theorem; Higher ramification theory; Explicit reciprocity laws; member US$62, Order code MEMO/198/927 Group extensions; Abstract class field theory; Weil groups; Bibliography. AMS Chelsea Publishing, Volume 366 January 2009, 192 pages, Hardcover, ISBN: 978-0-8218-4426-7, LC 2008042201, 2000 Mathematics Subject Classification: 11R37; New AMS-Distributed 11-01, 11R34, AMS members US$32, List US$35, Order code CHEL/366.H Publications

Probability Mathematical Physics

Moderate Deviations Boltzmann’s Legacy for the Range of Giovanni Gallavotti, University Planar Random Walks of Rome I, Italy, and Wolfgang L. Reiter and Jakob Yngvason, Richard F. Bass, University of University of Vienna, Austria, Connecticut, Storrs, CT, Xia Chen, Editors University of Tennessee, Knoxville, TN, and Jay Rosen, CUNY, Ludwig Eduard Boltzmann (1844–1906) College of Staten Island, NY was an Austrian physicist famous for his founding contributions in the fields Contents: Introduction; History; Overview; of statistical mechanics and statistical Preliminaries; Moments of the range; Moderate deviations thermodynamics. He was one of the most important advocates for atomic theory when that scientific model was still highly for Rn − ERn; Moderate deviations for ERn − Rn; Exponential asymptotics for the smoothed range; Exponential approximation; controversial. To commemorate the 100th anniversary of his death Laws of the iterated logarithm; Bibliography. in Duino, the International Symposium “Boltzmann’s Legacy” was held at the Erwin Schrödinger International Institute for Memoirs of the American Mathematical Society, Volume 198, Mathematical Physics in June 2006. Number 929 This text covers a broad spectrum of topics ranging from March 2009, 82 pages, Softcover, ISBN: 978-0-8218-4287-4, equilibrium statistical and nonequilibrium statistical physics, LC 2008047917, 2000 Mathematics Subject Classification: 60F10, ergodic theory and chaos to basic questions of biology and

February 2009 Notices of the AMS 317 New AMS-Distributed Publications

historical accounts of Boltzmann’s work. Besides the lectures presented at the symposium the volume also contains contributions specially written for this occasion. The articles give a broad Advertise in overview of Boltzmann’s legacy to the sciences from the standpoint of some of today’s leading scholars in the field. The book addresses students and researchers in mathematics, the Notices physics, and the history of science. This item will also be of interest to those working in general and of the American Mathematical Society interdisciplinary areas. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Contents: G. Gallavotti, Introduction; J. Renn, Boltzmann and the end of the mechanistic worldview; E. H. Lieb, What if Boltzmann had known about quantum mechanics; G. Gallavotti, Entropy, Target your nonequilibrium, chaos and infinitesimals; J. L. Lebowitz, From message time-symmetric microscopic dynamics to time-asymmetric macroscopic behavior: An overview; D. Ruelle, What physical to 30,000 quantities make sense in nonequilibrium statistical mechanics?; D. S. Ornstein, Boltzmann, ergodic theory, and chaos; active readers! C. Cercignani, 134 years of Boltzmann equation; C. Villani, H-theorem and beyond: Boltzman’s entropy in today’s mathematics; H. Spohn, On the Boltzmann equation for weakly nonlinear wave equations; E. G. Cohen, Entropy, probability and dynamics; C. Dellago and H. A. Posch, Realizing Boltzmann’s dream: computer simulations in modern statistical mechanics; A. Gabrielov, V. Keilis-Borok, Ya. Sinai, and I. Zaliapin, Statistical properties of the cluster dynamics of the systems of statistical mechanics; P. Schuster, Boltzmann and evolution: some basic Make an impact through questions of biology seen with atomistic glasses; W. L. Reiter, Ludwig Boltzmann—the restless prophet; Chronology; List of Display Advertising contributors; Name index; Subject index. Increase your sales and connect with new ESI Lectures in Mathematics and Physics, Volume 5 customers. October 2007, 284 pages, Hardcover, ISBN: 978-3-03719-057-9, The Notices of the AMS has the largest 2000 Mathematics Subject Classification: 01-02, 82-02, 82C03, circulation of any publication in the field. 82B40, AMS members US$62, List US$78, Order code EMSESILEC/5 Select premium positions are available. Target your audience through Classified Advertising An effective and economical way to get the most applicants for your open position. “We have been a long-time advertiser in the Notices and consider it a highly effective way to reach our customers in the mathematical community.” —Cambridge University Press

Please contact Anne Newcomb to create a program that will address your advertising needs. Anne Newcomb Phone: 401-455-4084 Email: [email protected]

Please visit our online media kit: http://www.ams.org/notices/adnot.htmlml

318 Notices of the AMS Volume 56, Number 2

Classified Advertisements Positions available, items for sale, services available, and more

Connecticut to undergraduate education on a small areas of pure and applied mathematics rural campus and potential for scholarly will be considered but preference will YALE UNIVERSITY work are essential. Applicants with math be given to analysis, algebra, differential education background or a willingness and algebraic geometry, mathematical Department of Mathematics to develop this expertise will be given physics, probability and statistics. Ap- The Mathematics Department at Yale favorable consideration. Teaching assign- plicants are required to have a Ph.D. in University intends to make one or more ment will include general education math mathematical sciences and be able to tenure-track assistant professor appoint- courses, probability, and statistics. Send develop a significant research program. ments beginning July 1, 2009. Positions letter, vita, unofficial transcripts, and 3 A strong commitment to undergraduate will be open to all fields of mathematics. letters of reference to: Dr. Marius Buliga, and graduate teaching is also required. Evidence of strong promise of leadership Math Search Committee, University of Duties include courses for undergraduate in research and excellence in teaching Pittsburgh at Bradford, 300 Campus Drive, students in natural sciences, engineering, required. Yale University is an Affirma- Bradford, PA 16701. http://www.upb. and economics; graduate courses in math- tive Action/Equal Opportunity Employer. pitt.edu/acadsearch.aspx. Review of ematics; and the eventual supervising of Yale values diversity among its faculty, completed applications will begin January undergraduate, master, or Ph.D. thesis. staff, and students and strongly encour- 15, 2009, and continue until position is The department offers internationally competitive salaries with start-up grants ages applications from women and un- filled. Pitt-Bradford is a beautiful, friendly for research. Proficiency in Spanish is derrepresented minorities. Please send campus with an emphasis on teaching. desirable. Please send an AMS standard curriculum vitae, description of research While faculty have the advantage of the cover sheet, curriculum vitae, research interests, and arrange for three letters of expansive resources and research oppor- plan, teaching statement, and three letters recommendation to be sent to: Tenure- tunities available through the University of recommendation to: Track Search Committee, Department of of Pittsburgh system, they also enjoy one- Mathematics, Yale University, P.O. Box on-one contact with their students in a se- Faculty Hiring 208283, New Haven, CT 06520-8283. Re- cure, personalized environment. Individu- Department of Mathematics view of applications will begin February als representing all aspects of diversity are Universidad de los Andes A.A. 4976 15, 2009. encouraged to apply. AA/EOE. 000016 000015 Bogotá, Colombia Electronic submission can also be sent to: [email protected]. Applicants interested in any further information Pennsylvania Colombia regarding the Mathematics Department at Los Andes please visit the website: UNIVERSITY OF PITTSBURGH AT UNIVERSIDAD DE LOS ANDES http://matematicas.uniandes.edu. BRADFORD Department of Mathematics co/. Preference will be given to applicants Department of Mathematics Faculty and visiting positions 2009 whose applications are submitted by Feb- ruary 11, 2009. Review of applications will Mathematics (assistant professor, ten- The Department of Mathematics invites continue until positions are filled. ure-stream), beginning fall 2009. Re- applications for positions at the tenure- 000012 quirements: Ph.D. or Ed.D. in math by track assistant professor level and visiting December 2009. A strong commitment professor to begin in August 2009. All

Suggested uses for classified advertising are positions available, books or ary 27, 2009; June/July 2009 issue–April 28. 2009; August 2009 issue–May 28, lecture notes for sale, books being sought, exchange or rental of houses, 2009; September 2009 issue–June 29, 2009. and typing services. U.S. laws prohibit discrimination in employment on the basis of color, The 2009 rate is $110 per inch or fraction thereof on a single column (one- age, sex, race, religion, or national origin. “Positions Available” advertise- inch minimum), calculated from top of headline. Any fractional text of 1/2 ments from institutions outside the U.S. may not be legally bound to inch or more will be charged at the next inch rate. No discounts for multiple conform to these or similar requirements. Details may be found on page ads or the same ad in consecutive issues. For an additional $10 charge, 1041 (volume 55). announcements can be placed anonymously. Correspondence will be Situations wanted advertisements from involuntarily unemployed math- forwarded. ematicians are accepted under certain conditions for free publication. Call Advertisements in the “Positions Available” classified section will be set toll-free 800-321-4AMS (321-4267) in the U.S. and Canada or 401-455-4084 with a minimum one-line headline, consisting of the institution name above worldwide for further information. body copy, unless additional headline copy is specified by the advertiser. Submission: Promotions Department, AMS, P.O. Box 6248, Providence, Headlines will be centered in boldface at no extra charge. Ads will appear Rhode Island 02940; or via fax: 401-331-3842; or send email to in the language in which they are submitted. [email protected]. AMS location for express delivery packages is There are no member discounts for classified ads. Dictation over the 201 Charles Street, Providence, Rhode Island 20904. Advertisers will be telephone will not be accepted for classified ads. billed upon publication. Upcoming deadlines for classified advertising are as follows: March 2009 issue–December 29, 2008; April 2009 issue–January 29, 2009; May 2009–Febru-

320 Notices of the AMS Volume 56, Number 2 AA WorldWorld WithoutWithout MatheMathemmaticaticss......

Courtesy of Map Collection, Yale University Library

AA WorldWorld WithWith MatheMathemmaticsatics

Support the future of mathematics Give to the American Mathematical Society Your donations support: Learn about giving opportunities and estate planning • Career paths of young mathematicians www.ams.org/giving-to-ams • Recognition of important work Contact the AMS Development • Public awareness and appreciation of Office 1.800.321.4267 mathematics (U.S. and Canada) or • Inspiration of young scholars 1.401.455.4000 (Epsilon Fund) (worldwide) email: [email protected] • International outreach 06/04 Meetings && Conferences of thethe AMSAMS

IMPORTANT information regarding meetings programs: AMS Sectional Meeting programs do not appear in the print version of the Notices. However, comprehensive and continually updated meeting and program information with links to the abstract for each talk can be found on the AMS website. See http://www.ams.org/meetings/. Final programs for Sectional Meetings will be archived on the AMS website accessible from the stated URL and in an electronic issue of the Notices as noted below for each meeting.

Jacob Lurie, Massachusetts Institute of Technology, On Urbana, Illinois topological quantum field theories. Gilles Pisier, Texas A&M University, Title to be an- University of Illinois at Urbana-Champaign nounced. Akshay Venkatesh, New York University-Courant In- March 27–29, 2009 stitute, Title to be announced. Friday – Sunday Special Sessions Meeting #1047 Algebra, Geometry and Combinatorics (Code: SS 10A), Central Section Rinat Kedem, University of Illinois at Urbana-Champaign, Associate secretary: Susan J. Friedlander and Alexander T. Yong, University of Minnesota. Announcement issue of Notices: January Algebraic Methods in Statistics and Probability (Code: SS Program first available on AMS website: February 12, 3A), Marlos A. G. Viana, University of Illinois at Chicago. 2009 Complex Dynamics and Value Distribution (Code: SS Program issue of electronic Notices: March 11A), Aimo Hinkkanen and Joseph B. Miles, University Issue of Abstracts: Volume 30, Issue 2 of Illinois at Urbana-Champaign. Deadlines Concrete Aspects of Real Positive Polynomials (Code: For organizers: Expired SS 20A), Victoria Powers, Emory University, and Bruce For consideration of contributed papers in Special Ses- Reznick, University of Illinois at Urbana-Champaign. sions: Expired Differential Geometry and Its Applications (Code: SS For abstracts: February 3, 2009 16A), Stephanie B. Alexander, University of Illinois at Urbana-Champaign, and Jianguo Cao, University of Notre The scientific information listed below may be dated. Dame. For the latest information, see www.ams.org/amsmtgs/ Geometric Function Theory and Analysis on Metric sectional.html. Spaces (Code: SS 6A), Sergiy Merenkov, Jeremy Taylor Tyson, and Jang-Mei Wu, University of Illinois at Urbana- Invited Addresses Champaign. Jeffrey C. Lagarias, University of Michigan, From Geometric Group Theory (Code: SS 2A), Sergei V. Iva- Apollonian circle packings to Fibonacci Numbers (Erdo˝s nov, Ilya Kapovich, Igor Mineyev, and Paul E. Schupp, Memorial Lecture). University of Illinois at Urbana-Champaign.

322 Notices of the AMS Volume 56, Number 2 Meetings & Conferences

Graph Theory (Code: SS 4A), Alexander V. Kostochka and Douglas B. West, University of Illinois at Urbana- Raleigh, North Champaign. Holomorphic and CR Mappings (Code: SS 9A), John P. Carolina D’Angelo, Jiri Lebl, and Alex Tumanov, University of Il- North Carolina State University linois at Urbana-Champaign. Hyperbolic Geometry and Teichmüller Theory (Code: April 4–5, 2009 SS 18A), Jason Deblois, University of Illinois at Chicago, Saturday – Sunday Richard P. Kent IV, Brown University, and Christopher J. Leininger, University of Illinois at Urbana-Champaign. Meeting #1048 Local and Homological Methods in Commutative Algebra Southeastern Section (Code: SS 13A), Florian Enescu, Georgia State University, Associate secretary: Matthew Miller and Sandra Spiroff, University of Mississippi. Announcement issue of Notices: January 2009 Program first available on AMS website: February 19, Mathematical Visualization (Code: SS 7A), George K. 2009 Francis, University of Illinois at Urbana-Champaign, Louis Program issue of electronic Notices: April 2009 H. Kauffman, University of Illinois at Chicago, Dennis Mar- Issue of Abstracts: Volume 30, Issue 2 tin Roseman, University of Iowa, and Andrew J. Hanson, Indiana University. Deadlines Nonlinear Partial Differential Equations and Applica- For organizers: Expired tions (Code: SS 21A), Igor Kukavica, University of Southern For consideration of contributed papers in Special Ses- California, and Anna L. Mazzucato, Pennsylvania State sions: Expired University. For abstracts: February 10, 2009 Number Theory in the Spirit of Erdo˝s (Code: SS 14A), The scientific information listed below may be dated. Kevin Ford and A. J. Hildebrand, University of Illinois at For the latest information, see www.ams.org/amsmtgs/ Urbana-Champaign. sectional.html. Operator Algebras and Operator Spaces (Code: SS 8A), Zhong-Jin Ruan, Florin P. Boca, and Marius Junge, Uni- Invited Addresses versity of Illinois at Urbana-Champaign. Nathan Dunfield, University of Illinois at Urbana- Probabilistic and Extremal Combinatorics (Code: SS 5A), Champaign, Surfaces in finite covers of 3-manifolds: The Jozsef Balogh and Zoltan Furedi, University of Illinois at virtual Haken conjecture. Reinhard C. Laubenbacher, Virginia Bioinformatics Urbana-Champaign. Institute, Algebraic models in systems biology. The Interface Between Number Theory and Dynamical Jonathan C. Mattingly, Duke University, Stochasti- Systems (Code: SS 17A), Florin Boca, University of Illinois cally forced fluid equations: Transfer between scales and at Urbana-Champaign, Jeffrey Lagarias, University of ergodicity. Michigan, and Kenneth Stolarsky, University of Illinois Raman Parimala, Emory University, Arithmetic of linear at Urbana-Champaign. algebraic groups over 2-dimensional geometric fields. The Logic and Combinatorics of Algebraic Structures Michael S. Waterman, University of Southern California, (Code: SS 22A), John Snow, Concordia University, and Reading DNA sequences: Twenty-first century technology Jeremy Alm, Illinois College. with eighteenth century mathematics (Einstein Public Lec- ture in Mathematics). Time, Scale, and Frequency Methods in Harmonic Analysis (Code: SS 15A), Richard S. Laugesen, University Special Sessions of Illinois at Urbana-Champaign, and Darrin M. Speegle, Advancements in Turbulent Flow Modeling and Compu- St. Louis University. tation (Code: SS 8A), Leo G. Rebholz, Clemson University, Topological Dynamics and Ergodic Theory (Code: SS and Traian Iliescu, Virginia Polytechnic Institute and State 19A), Alica Miller, University of Louisville, and Joseph University. Rosenblatt, University of Illinois at Urbana-Champaign. Algebraic Groups and Symmetric Spaces (Code: SS 19A), Topological Field Theories, Representation Theory, and Stacy Beun, Cabrini College, and Aloysius Helminck, North Carolina State University. Algebraic Geometry (Code: SS 12A), Thomas Nevins, Applications of Algebraic and Geometric Combinatorics University of Illinois at Urbana-Champaign, and David (Code: SS 2A), Seth M. Sullivant, Harvard University, and Ben-Zvi, University of Texas at Austin. Carla D. Savage, North Carolina State University. q-Series and Partitions (Code: SS 1A), Bruce Berndt, Applications of Dynamical Systems to Problems in Biol- University of Illinois at Urbana-Champaign, and Ae Ja Yee, ogy (Code: SS 16A), John E. Franke and James F. Selgrade, Pennsylvania State University. North Carolina State University.

February 2009 Notices of the AMS 323 Meetings & Conferences

Brauer Groups, Quadratic Forms, Algebraic Groups, and Lie Algebras (Code: SS 12A), Eric S. Brussel and Skip San Francisco, Garibaldi, Emory University. Commutative Rings and Monoids (Code: SS 17A), Scott California T. Chapman, Sam Houston State University, and James B. Coykendall, North Dakota State University. San Francisco State University Computational Methods in Lie Theory (Code: SS 10A), Eric Sommers, University of Massachusetts, Amherst, and April 25–26, 2009 Molly Fenn, North Carolina State University. Saturday – Sunday Deferred Correction Methods and their Applications (Code: SS 20A), Elizabeth L. Bouzarth and Anita T. Layton, Meeting #1049 Duke University. Western Section Enumerative Geometry and Related Topics (Code: SS Associate secretary: Michel L. Lapidus 7A), Richard L. Rimanyi, University of North Carolina, Announcement issue of Notices: February 2009 Chapel Hill, and Leonardo C. Mihalcea, Duke University. Program first available on AMS website: March 12, 2009 Galois Module Theory and Hopf Algebras (Code: SS 13A), Program issue of electronic Notices: April 2009 Robert G. Underwood, Auburn University Montgomery, Issue of Abstracts: Volume 30, Issue 3 and James E. Carter, College of Charleston. Geometry of Differential Equations (Code: SS 9A), Deadlines Thomas A. Ivey, College of Charleston, and Irina A. For organizers: Expired Kogan, North Carolina State University. For consideration of contributed papers in Special Ses- Homotopical Algebra with Applications to Mathemati- sions: Expired cal Physics (Code: SS 3A), Thomas J. Lada, North Carolina For abstracts: March 3, 2009 State University, and Jim Stasheff, University of North Carolina, Chapel Hill. The scientific information listed below may be dated. Kac-Moody Algebras, Vertex Algebras, Quantum Groups, For the latest information, see www.ams.org/amsmtgs/ and Applications (Code: SS 1A), Bojko N. Bakalov, Kai- sectional.html. lash C. Misra, and Naihuan N. Jing, North Carolina State Invited Addresses University. Yehuda Shalom, University of California Los Angeles, Low-Dimensional Topology and Geometry (Code: SS Title to be announced. 4A), Nathan M. Dunfield, University of Illinois at Urbana- Roman Vershynin, University of California Davis, Title Champaign, John B. Etnyre, Georgia Institute of Technol- to be announced. ogy, and Lenhard Ng, Duke University. Karen Vogtmann, Cornell University, Title to be an- Mathematical Progress and Challenges for Biological Ma- nounced. terials (Code: SS 18A), Mansoor A. Haider, North Carolina Efim Zelmanov, University of California Los Angeles, State University, and Gregory Forest, University of North Title to be announced. Carolina, Chapel Hill. Mathematics of Immunology and Infectious Diseases Special Sessions (Code: SS 14A), Stanca M. Ciupe, Duke University. Advances in the Theory of Integer Linear Optimization Nonlinear Dynamics and Control (Code: SS 11A), An- and its Extensions (Code: SS 7A), Matthias Koeppe and thony M. Bloch, University of Michigan, Ann Arbor, and Peter Malkin, University of California Davis. Dmitry Zenkov, North Carolina State University. Algebra and Number Theory with Polyhedra (Code: SS Numerical Solution of Partial Differential Equations and 11A), Matthias Beck, San Francisco State University, and Applications (Code: SS 15A), Alina Chertock and Zhilin Li, Christian Haase, Freie Universität Berlin. North Carolina State University. Applications of Knot Theory to the Entanglement of Recent Advances in Symbolic Algebra and Analysis Biopolymers (Code: SS 10A), Javier Arsuaga, San Francisco (Code: SS 5A), Michael F. Singer and Agnes Szanto, North State University, Kenneth Millett, University of California Carolina State University. Santa Barbara, and Mariel Vazquez, San Francisco State Rings, Algebras, and Varieties in Combinatorics (Code: University. SS 6A), Patricia Hersh, North Carolina State University, Aspects of Differential Geometry (Code: SS 9A), David Christian Lenart, SUNY Albany, and Nathan Reading, Bao, San Francisco State University, and Lei Ni, University North Carolina State University. of California San Diego. Stochastic Dynamics (Code: SS 21A), Yuri Bakhtin, Banach Algebras, Topological Algebras and Abstract Georgia Institute of Technology, and Scott McKinley and Harmonic Analysis (Code: SS 1A), Thomas V. Tonev, Uni- Jonathan C. Mattingly, Duke University. versity of Montana-Missoula, and Fereidoun Ghahramani, The Mathematics of Biochemical Reaction Networks University of Manitoba. (Code: SS 22A), Anne Shiu, University of California Berkeley, Concentration Inequalities (Code: SS 3A), Sourav Chat- Manoj Gopalkrishnan, University of Southern California, terjee, University of California Berkeley, and Roman Ver- and Gheorghe Craciun, University of Wisconsin-Madison. shynin, University of California Davis.

324 Notices of the AMS Volume 56, Number 2 Meetings & Conferences

Geometry and Topology of Orbifolds (Code: SS 6A), Eliza- Local Information beth Stanhope, Lewis & Clark University, and Joseph E. Please visit the Web sites maintained by San Francisco Borzellino, California State University San Luis Obispo. State University at http://www.sfsu.edu, the Depart- Lie Group Actions, Teichmüller Flows and Number ment of Mathematics at http://math.sfsu.edu and Theory (Code: SS 12A), Jayadev Athreya, Yale University, the site maintained by the San Francisco Convention and Yitwah Cheung, San Francisco State University, and Anton Visitors Bureau at http://www.sfvisitor.org. Zorich, Rennes University. Matroids in Algebra and Geometry (Code: SS 8A), Fed- Other Activities erico Ardila, San Francisco State University, and Lauren AMS Editorial Activity: An acquisitions editor from the Williams, Harvard University. AMS book program will be present to speak with prospec- Nonlinear Dispersive Equations (Code: SS 4A), Sebastian tive authors. If you have a book project that you would Herr, University of California Berkeley, and Jeremy L. like to discuss with the AMS, please stop by the book Marzuola, Columbia University. exhibit. Nonlinear Partial Differential Equations (Code: SS 13A), Book Sales: Stop by the on-site AMS Bookstore and Igor Kukavica, Amjad Tuffaha, and Mohammed Ziane, review the newest titles from the AMS, enjoy up to 25% University of Southern California. off all AMS publications, or take home an AMS t-shirt! Recent Progress in Geometric Group Theory (Code: SS Complimentary coffee will be served courtesy of AMS 2A), Seonhee Lim and Anne Thomas, Cornell Univer- Membership Services. sity. Parking Accommodations Parking is available in the university parking structure Participants should make their own arrangements directly located on South State Street. For more information with a hotel of their choice. Rates quoted do not include regarding parking please visit http://www.sfsu.edu/ sales tax. The AMS is not responsible for rate changes or %7Eparking/text/tocampus.html. for the quality of the accommodations. When making a reservation, participants should state they are with the Registration and Meeting Information American Mathematical Society group (AMS Meeting). The registration desk will be located on the third (main) None of the hotels listed are within walking distance of the floor of Thornton Hall, and will be open from 7:30 a.m. to meeting. Cancellation and early checkout policies vary; be 4:00 p.m. on Saturday and 8:00 a.m. to noon on Sunday. sure to check when you make your reservation. Talks will take place in the Science Building and Thornton The Great Highway Inn, 1234 Great Highway, San Hall. Francisco, CA, 94112; 800-624-6644, 415-731-6644, fax: Registration fees are US$40 for AMS or CMS members, 415-731-5309. Rates are $110/single and $135/double US$60 for nonmembers; and US$5 for students, unem- plus tax. Cancellation policy requires a 48-hour notice. ployed mathematicians, and emeritus members. Fees are Cancellation and early checkout policies vary; be sure to payable on site by cash, check, or credit card. check when you make your reservation. Hampton Inn, 2700 Junipero Serra Blvd, Daly City, CA; Travel Information and Campus Map 650-755-7500 or 866-519-4851. Rates are $119 single/ San Francisco Airport (SFO): From the departure area double plus tax. All terms and conditions are subject take the I-280 North entrance. Take I-280 North, exit at to availability. The Hampton Inn is located on Junipero 19th Avenue. Take Junipero Serra Boulevard to Holloway Serra Blvd. just two miles south of the campus. All rooms Avenue; turn left on Holloway Avenue to campus at 19th include telephone with complimentary local calls, data Avenue. ports, cable television, and hairdryers. Free parking on To get to the parking garage, continue on Holloway property, hot breakfast, and heated pool are also included. Ave. to Font Blvd. Turn right onto Font Blvd. and continue Deadline for reservations is March 1. Cancellation and to Lake Merced Blvd. Turn right onto Lake Merced Blvd. early checkout policies vary; be sure to check when you then take an immediate right onto State Drive which is the make your reservation. entrance to the parking garage. Sheraton Gateway Hotel–San Francisco Airport, 600 By Public Transportation: BART: Exit the Daly City BART Airport Blvd., Burlingame, CA 94010; 650-340-8500, Station then take the SFSU shuttle or the MUNI 28 bus. http://www.sheratonsfo.com. Rates are $105 single/ SuperShuttle: Call 800-258-3826 for reservations or double plus tax. There is an additional $15 fee per person find SuperShuttle vans outside of Departures. for triple or quad occupancy. Deadline for reservations By Car: is April 3. Cancellation and early checkout policies vary; From the North: Take Highway 101 South, cross the be sure to check when you make your reservation. Golden Gate Bridge. Take 19th Avenue/Highway 1 exit. Follow 19th Avenue to campus at Holloway Avenue. Food Service To get to the parking garage, turn right onto Holloway A list of restaurants will be available at the registration Ave. and continue to Font Blvd. Turn right onto Font Blvd. desk. and continue to Lake Merced Blvd. Turn right onto Lake

February 2009 Notices of the AMS 325 Meetings & Conferences

Merced Blvd. then take an immediate right onto State Drive US.html and http://travel.state.gov/visa/index. which is the entrance to the parking garage. html http://travel.state.gov/visa/visa_1750. From the South: Take I-280 North, exit at 19th Avenue. html. If you need a preliminary conference invitation in Take Junipero Serra Boulevard to Holloway Avenue, turn order to secure a visa, please send your request to wsd@ left on Holloway Avenue to campus at 19th Avenue. ams.org. To get to the parking garage, continue on Holloway If you discover you do need a visa, the National Acad- Ave. to Font Blvd. Turn right onto Font Blvd. and continue emies website (see above) provides these tips for success- to Lake Merced Blvd. Turn right onto Lake Merced Blvd. ful visa applications: then take an immediate right onto State Drive which is the * Visa applicants are expected to provide evidence that entrance to the parking garage. they are intending to return to their country of residence. From the East: Take I-80 West across the Bay Bridge Therefore, applicants should provide proof of “binding” to Highway 101 South. Take 101 South to I-280 toward or sufficient ties to their home country or permanent Daly City. Take the San Jose Avenue/Mission St. exit (im- residence abroad. This may include documentation of mediately after the Ocean Avenue exit), bearing right onto the following: Sagamore Street to Brotherhood Way to Junipero Serra - family ties in home country or country of legal per- Boulevard North. Take Junipero Serra Boulevard to Hol- manent residence loway Avenue, turn left on Holloway Avenue to campus - property ownership at 19th Avenue. To get directly to the parking garage stay on Brother- - bank accounts hood Way and turn right onto Lake Merced Blvd. Turn right - employment contract or statement from employer onto State Drive which is the third light after turning onto stating that the position will continue when the employee Lake Merced Blvd. and immediately after Font Blvd. returns; Click here http://www.sfsu.edu/%7Eparking/ * Visa applications are more likely to be successful if images/parking_map.gif or visit http://www.sfsu. done in a visitor’s home country than in a third country; edu/%7Eparking/text/tocampus.html for a campus * Applicants should present their entire trip itinerary, map. including travel to any countries other than the United States, at the time of their visa application; Car Rental * Include a letter of invitation from the meeting orga- Avis Rent A Car is the official car rental company for the nizer or the U.S. host, specifying the subject, location and meeting. Depending on variables such as location, length dates of the activity, and how travel and local expenses of rental, and size of vehicle, Avis will offer participants will be covered; the best available rate which can range from 5%–25% dis- * If travel plans will depend on early approval of the visa count off regular rates. Participants must use the assigned application, specify this at the time of the application; Meeting Avis Discount Number (J098887) and meet Avis * Provide proof of professional scientific and/or rate requirements to receive the discount. (Rate discounts educational status (students should provide a university are available at all corporate and participating licensee transcript). locations.) Reservations can be made by calling 800-331- This list is not to be considered complete. Please visit 1600 or online at http://www.avis.com. the websites above for the most up-to-date information. All car rentals include unlimited free mileage and are available to renters 25 years and older. Renters must also meet Avis’s driver and credit requirements. Return to the same rental location or additional surcharges may apply. Worcester, Rates do not include any state or local surcharges, tax, optional coverages, or gas refueling charges. Massachusetts Weather Worcester Polytechnic Institute The weather in April is variable, with temperatures from April 25–26, 2009 70° Fahrenheit to 85° Fahrenheit. The weather can turn cold, overcast, and windy due to the close proximity of Saturday – Sunday the SFSU campus to the ocean. Meeting #1050 Special Travel Information for International Eastern Section Participants Associate secretary: Steven H. Weintraub Visa regulations are continually changing for travel to the Announcement issue of Notices: February 2009 United States. Visa applications may take from three to Program first available on AMS website: March 12, 2009 four months to process and require a personal interview, Program issue of electronic Notices: April 2009 as well as specific personal information. International Issue of Abstracts: Volume 30, Issue 3 participants should view the important information about traveling to the U.S. found at http://www7. Deadlines nationalacademies.org/visas/Traveling_to_ For organizers: Expired

326 Notices of the AMS Volume 56, Number 2 Meetings & Conferences

For consideration of contributed papers in Special Ses- American Mathematical Society or AMS. The AMS is not sions: Expired responsible for rate changes or for the quality of the ac- For abstracts: March 3, 2009 commodations. Hotels have varying cancellation or early checkout penalties; be sure to ask for details when making The scientific information listed below may be dated. your reservation. For the latest information, see www.ams.org/amsmtgs/ Because of several large events in the area at the time of sectional.html. our meeting, hotel availability is limited. We have secured room blocks at the following two hotels. To guarantee a Invited Addresses room reservation, we advise making your travel plans Octav Cornea, Université de Montréal, Lagrangian early. submanifolds: From physics to number theory. Courtyard by Marriott Worcester, 72 Grove Street, Fengbo Hang, Courant Institute of New York University, Worcester, MA 01605; 508-363-0300, toll free: 888-887- Topology of weakly differentiable maps. 7948; fax: 508-363-3563; http://www.marriott.com/ Umberto Mosco, Worcester Polytechnic Institute, Frac- hotels/travel/boswr-courtyard-worcester/. The tal spectra between Scylla and Charybdis. hotel is approximately 0.69 miles from the meeting site. Kevin Whyte, University of Illinois at Chicago, A rapid Rates start at US$116 per night. Rates quoted do not in- survey of coarse geometry. clude the sales and occupancy tax of 12%. Be sure to check cancellation and early checkout policies. Amenities include Special Sessions spacious hotel rooms featuring new luxury bedding, large Algebraic Graph Theory, Association Schemes, and Re- workspaces, free wireless high speed Internet access, in- lated Topics (Code: SS 8A), William J. Martin, Worcester door pool, whirlpool, exercise room, cozy fireplace lounge, Polytechnic Institute, and Sylvia A. Hobart, University of restaurant serving breakfast, and complimentary on-site Wyoming. parking. Deadline for reservations is April 3, 2009. Analysis of Weakly Differentiable Maps with Constraints Beechwood Hotel, 363 Plantation Street, Worcester, and Applications (Code: SS 11A), Fengbo Hang, Courant MA 01605, 508-754-0731; toll free: 800-344-2589; fax: Institute, New York University, and Mohammad Reza 508-754-0731; http://www.beechwoodhotel.com/. This Pakzad, University of Pittsburgh. luxury hotel is located approximately 2.34 miles from Discrete Geometry and Combinatorics (Code: SS 5A), the meeting site. Rates start at US$149 per night. Rates Egon Schulte, Northeastern University, and Brigitte Ser- quoted do not include the sales and occupancy tax of 12%. vatius, Worcester Polytechnic Institute. Be sure to check cancellation and early checkout policies. Effective Dynamics and Interactions of Localized Struc- Amenities include complimentary continental breakfast tures in Schrödinger Type Equations (Code: SS 10A), Fri- and newspapers, free wireless high speed Internet, jogging dolin Ting, Lakehead University. track and fitness center. Complimentary parking and fine Number Theory (Code: SS 4A), John T. Cullinan, Bard dining restaurant are on site. Deadline for reservations College, and Siman Wong, University of Massachusetts, is March 27, 2009. Amherst. Quasi-Static and Dynamic Evolution in Fracture Me- Below is a list of other hotels in the area that may have chanics (Code: SS 6A), Christopher J. Larsen, Worcester a small number of rooms available. No rooms were specifi- Polytechnic Institute. cally reserved for participants at these hotels. Real and Complex Dynamics of Rational Difference Crowne Plaza Hotel Worcester, 10 Lincoln Square, Equations with Applications (Code: SS 9A), M. R. S. Kule- Worcester, MA 01608; 508-791-1600; toll free: 877-227- novic and Orlando Merino, University of Rhode Island. 6963; fax: 508-7911796; http://www.ichotelsgroup. Scaling, Irregularities, and Partial Differential Equations com/h/d/cp/1/en/hotel/wrccp?_requestid=3046986. (Code: SS 7A), Umberto Mosco and Bogdan M. Vernescu, The hotel is located approximately 0.75 miles from the Worcester Polytechnic Institute. meeting site. Amenities include health club facilities, Symplectic and Contact Topology (Code: SS 1A), Peter indoor and outdoor pools, jacuzzi/hot tub, and free wire- Albers, Purdue University/ETH Zurich, and Basak Gurel, less access; parking garage is available on site with a fee Vanderbilt University. of US$5 for self parking or US$8 for valet. The Mathematics of Climate Change (Code: SS 3A), Cath- Hilton Garden Inn Worcester, 35 Major Taylor Boule- erine A. Roberts and Gareth E. Roberts, College of the vard, Worcester, MA 01608, 508-753-5700; fax: 508- 753- Holy Cross, and Mary Lou Zeeman, Bowdoin College. 5780; http://hiltongardeninn.hilton.com/en/gi/ Topological Robotics (Code: SS 2A), Li Han and Lee N. hotels/index.jhtml;jsessionid=UU500HMBPAQW0C Rudolph, Clark University. SGBJC32EQ?ctyhocn=BEDWOGI. The hotel is located approximately one mile from the meeting site. Amenities Accommodations include well-appointed guest rooms with large work desk; Participants should make their own arrangements directly complimentary high speed Internet; fitness room; pool; with the properties listed below. Special rates for the onsite dining: Great American Grill and Uno Chicago Grill; meeting are available at the properties shown below for and parking garage across from hotel with a daily fee of Friday and Saturday nights. When making reservations US$8.95. Valet parking is also available daily from 6:00 participants should state that they are a guest of the a.m–11:00 p.m. with a fee of US$12.95.

February 2009 Notices of the AMS 327 Meetings & Conferences

Hampton Inn Worcester, 110 Summer Street, Worces- Transportation ter, MA 01608, 508-757-0400, fax: 508-831-9839; http:// By air: hamptoninn.hilton.com/en/hp/hotels/index. Logan International Airport in Boston, MA (http:// jhtml?ctyhocn=WORMAHX. The hotel is located approxi- www.massport.com/logan/default.aspx) is approximately 1.09 miles from the meeting site. Amenities include mately 46 miles from the Worcester campus. The approxi- free breakfast buffet, complimentary high speed Internet, mate taxicab fare is US$120. You may also get to Worcester complimentary parking, and exercise room. via the commuter rail system. For fare information, maps, and schedules, visit the MBTA Commuter Rail website Food Service http://www.mbta.com/schedules\_and\_maps/rail/ The campus center is open all day Saturday, 8:00 a.m.–1:00 or call 617-222-3200. a.m. and Sunday, 8:00 a.m.–12:00 midnight. Eating facili- T. F. Green Airport in Providence, R. I. (http://www. ties include 48 Café Dunkin Donuts: 8:00 a.m.–6:00 p.m.; pvdairport.com/) is approximately 51 miles from the Campus Center Food Court: Saturday, 11:30 a.m.–12:00 Worcester campus; approximate cab fare is US$118. See midnight and Sunday 11:30 a.m.–11:00 p.m.; The Goat’s below for shuttle service information. Head Restaurant: Saturday: 11:00 a.m.–1:00 a.m. and Manchester Airport in Manchester, N. H. (http:// Sunday: 11:00 a.m.–11:00 p.m. Within walking distance www.flymanchester.com) is approximately 69 miles from or a short drive one can find a variety of choices for din- the Worcester campus; approximate cab fare is US$162. ing at http://www.wpi.edu/About/Visitors/dining. Renting a car is advised as there is no discount shuttle html. Additional information and recommendations will service available. be provided on site. Airport Shuttles: Knight’s Airport Limousine Service (800-822-5456, Local Information http://www.knightsairportlimo.com/) provides The WPI visitors guide featuring directions and a cam- transportation to and from Logan Airport and T. F. Green pus map can be found at http://www.wpi.edu/About/ Airport. One-way transportation is approximately US$66 Visitors/index.html. from T. F. Green Airport and approximately US$55 from Logan Airport. Reservations should be made 24 hours Other Activities prior to pickup. Visit their website for rates and reserva- AMS Book Sale: Stop by the on-site AMS Bookstore and tions. review the newest titles from the AMS, enjoy up to 25% By bus: off all AMS publications, or take home an AMS T-shirt! The city of Worcester is served by two bus companies, Complimentary coffee will be served courtesy of AMS Greyhound Lines, Inc. (http://www.greyhound.com) and Peter Pan Bus Lines (http://www.peterpanbus.com). Membership Services. For Greyhound fares and schedule information, call 800- AMS Editorial Activity: An acquisitions editor from 231-2222. For Peter Pan fares and schedule information, the AMS book program will be present to speak with call 800-343-9999. prospective authors. If you have a book project that you Commuter Rail would like to discuss with the AMS, please stop by the The MBTA Commuter Rail stop located on Shrewsbury book exhibit. Street in Worcester is about 1.5 miles away from campus. Parking The stop is at the end of the Worcester/Framingham line. For fare information, maps, and schedules, visit the There are numerous campus lots available for parking on MBTA Commuter Rail website http://www.mbta.com/ the weekends as well as on-street parking. The quadrangle schedules_and_maps/rail/ or call 617-222-3200. area is not available on the weekend. The lots for park- Taxi Services ing are Higgins House, Gordon Library, West Street, and Two taxi services provide transportation in the Worces- Stoddard Complex. Please see campus map for location ter area: Yellow Cab, 508-754-3211; and Red Cab, 508-792- and directions. http://www.wpi.edu/About/Visitors/ 9999 & 508-756-9000. campusmap.html. Trains Amtrak services the city of Worcester from over 500 cit- Registration and Meeting Information ies nationwide. The Worcester Amtrak station is located on The meetings will be held in Higgins Labs and Salisbury Shrewsbury Street, about 1.5 miles from the campus. For Labs at Worcester Polytechnic Institute, Worcester, MA. more information, visit the Amtrak website http://www. The registration desk and book exhibit will be located in amtrak.com or call 800-872-7245. the Price Conference Room, Higgins Labs 102. The desk Driving Directions will be open Saturday, April 25, from 7:30 a.m. until 4:00 Worcester Campus, 100 Institute Road, Worcester, MA p.m. and Sunday, April 26, from 8:00 a.m. until noon. 01609-2280. Fees are US$40/AMS or CMS members; US$60/nonmem- From the East bers; US$5/emeritus members, students, or unemployed Take Mass. Turnpike (I-90) to Exit 11A (I-495). Proceed mathematicians. Fees are payable by cash, check, VISA, north to exit 25B (I-290), then west into Worcester. Take MasterCard, Discover, or American Express. Exit 18 (Lincoln Sq., Rte. 9), turn right at end of ramp,

328 Notices of the AMS Volume 56, Number 2 Meetings & Conferences then an immediate right before next traffic light. At next order to secure a visa, please send your request to wsd@ light, proceed straight through, bearing to the right on ams.org. Salisbury St. At the WPI sign, turn left onto Boynton St., If you discover you do need a visa, the National Acad- then right onto Institute Rd. Take your first right (Private emies website (see above) provides these tips for success- Way). Admissions visitor parking is located on either side ful visa applications: of Bartlett Center, the building that is directly ahead as * Visa applicants are expected to provide evidence that you enter the Quadrangle area; general visitor parking is they are intending to return to their country of residence. on the right as you approach the Quadrangle, adjacent to Therefore, applicants should provide proof of “binding” Alumni Gymnasium. Admissions visitors should pick up or sufficient ties to their home country or permanent a visitor parking pass at the Admissions Office to display residence abroad. This may include documentation of in their windshield. the following: From the North - family ties in home country or country of legal per- Take I-495 south to I-290. Follow directions from manent residence east. - property ownership From the South and West - bank accounts Take Mass. Turnpike (I-90) to Exit 10 (Auburn). Proceed - employment contract or statement from employer east on I-290 into Worcester. Take Exit 17 (Lincoln Sq., Rte. stating that the position will continue when the employee 9), turn left at end of ramp, follow Rte. 9 west through Lin- returns; coln Sq., straight onto Highland St., then right at light onto * Visa applications are more likely to be successful if West St. Travel one block and cross Institute Road (onto done in a visitor’s home country than in a third country; Private Way). Admissions visitor parking is located on * Applicants should present their entire trip itinerary, either side of Bartlett Center, the building that is directly including travel to any countries other than the United ahead as you enter the Quadrangle area; general visitor States, at the time of their visa application; parking is on the right as you approach the Quadrangle, * Include a letter of invitation from the meeting orga- adjacent to Alumni Gymnasium. Admissions visitors nizer or the U.S. host, specifying the subject, location and should pick up a visitor parking pass at the Admissions dates of the activity, and how travel and local expenses Office to display in their windshield. will be covered; Information on public transportation is also available. * If travel plans will depend on early approval of the visa Avis Rent A Car is the official car rental company application, specify this at the time of the application; for the meeting. Depending on variables such as location, length of rental, and size of vehicle, Avis will offer * Provide proof of professional scientific and/or participants the best available rate which can range from educational status (students should provide a university 5%–25% discount off regular rates. Participants must use transcript). the assigned Meeting Avis Discount Number (J098887) and This list is not to be considered complete. Please visit meet Avis rate requirements to receive the discount. (Rate the websites above for the most up-to-date information. discounts are available at all corporate and participating licensee locations.) Reservations can be made by calling 800-331-1600 or online at http://www.avis.com. Waco, Texas All car rentals include unlimited free mileage and are available to renters 25 years and older. Renters must also Baylor University meet Avis’s driver and credit requirements. Return to the October 16–18, 2009 same rental location Friday – Sunday Weather Meeting #1051 This time of year the temperature varies a good deal but typically offers mid-60° days followed by brisk evenings. Central Section Associate secretary: Susan J. Friedlander Special Travel Information for International Announcement issue of Notices: August 2009 Participants Program first available on AMS website: September 3, Visa regulations are continually changing for travel to the 2009 United States. Visa applications may take from three to Program issue of electronic Notices: October 2009 four months to process and require a personal interview, Issue of Abstracts: Volume 30, Issue 4 as well as specific personal information. International participants should view the important information Deadlines about traveling to the U.S. found at http://www7. For organizers: March 17, 2009 nationalacademies.org/visas/Traveling_to_ For consideration of contributed papers in Special Ses- US.html and http://travel.state.gov/visa/index. sions: June 30, 2009 html http://travel.state.gov/visa/visa_1750. For abstracts: August 25, 2009 html. If you need a preliminary conference invitation in

February 2009 Notices of the AMS 329 Meetings & Conferences

The scientific information listed below may be dated. For consideration of contributed papers in Special Ses- For the latest information, see www.ams.org/amsmtgs/ sions: July 7, 2009 sectional.html. For abstracts: September 1, 2009

Invited Addresses The scientific information listed below may be dated. David Ben-Zvi, University of Texas at Austin, Title to For the latest information, see www.ams.org/amsmtgs/ be announced. sectional.html. Alexander A. Kiselev, University of Wisconsin, Title to Invited Addresses be announced. Michael C. Reed, Duke University, Title to be an- Michael K. H. Kiessling, Rutgers University, Title to be nounced. announced. Igor Rodnianski, Princeton University, Title to be an- Kevin R. Payne, Universita degli di Milano, Title to be nounced. announced. Laurent Saloff-Coste, Cornell University, Title to be Special Sessions announced. Robert C. Vaughan, Penn State University, Title to be Commutative Algebra: Module and Ideal Theory (Code: announced. SS 4A), Lars W. Christensen, Texas Tech University, Louiza Fouli, University of Texas at Austin, and David Jorgensen, Special Sessions University of Texas at Arlington. Homotopy Theory (code: SS 1A), James Gillespie and Dynamic Equations on Time Scales: Analysis and Ap- Mark W. Johnson, Pennsylvania State University, Simona plications (Code: SS 1A), John M. Davis, Ian A. Gravagne, Paoli, University of Haifa, Donald Yau, Ohio State Uni- and Robert J. Marks, Baylor University. versity. Lie Groups, Lie Algebras, and Representations (Code: Difference Equations and Applications (code: SS 2A), SS 6A), Markus Hunziker, Mark Sepanski, and Ronald Michael A. Radin, Rochester Institute of Technology. Stanke, Baylor University. Mathematical Models of Neuronal and Metabolic Mecha- nisms (Code: SS 3A), Janet Best, Ohio State University, and Boca Raton, Florida Michael Reed, Duke University. Numerical Solutions of Singular or Perturbed Partial Florida Atlantic University Differential Equation Problems with Applications (Code: SS 2A), Peter Moore, Southern Methodist University, and October 30 – November 1, 2009 Qin Sheng, Baylor University. Friday – Sunday Topological Methods for Boundary Value Problems for Ordinary Differential Equations (Code: SS 5A), Richard Meeting #1053 Avery, Dakota State University, Paul W. Eloe, University Southeastern Section of Dayton, and Johnny Henderson, Baylor University. Associate secretary: Matthew Miller Announcement issue of Notices: August 2009 Program first available on AMS website: September 17, 2009 University Park, Program issue of electronic Notices: October 2009 Pennsylvania Issue of Abstracts: Volume 30, Issue 4 Deadlines Pennsylvania State University For organizers: March 30, 2009 October 24–25, 2009 For consideration of contributed papers in Special Ses- sions: July 14, 2009 Saturday – Sunday For abstracts: September 8, 2009 Meeting #1052 The scientific information listed below may be dated. Eastern Section For the latest information, see www.ams.org/amsmtgs/ Associate secretary: Steven H. Weintraub sectional.html. Announcement issue of Notices: August 2009 Program first available on AMS website: September 10, Invited Addresses 2009 Spyros Alexakis, Princeton University, Title to be an- Program issue of electronic Notices: October 2009 nounced. Issue of Abstracts: Volume 30, Issue 4 Kai-Uwe Bux, University of Virginia, Title to be announced. Deadlines Dino J. Lorenzini, University of Georgia, Title to be For organizers: March 24, 2009 announced.

330 Notices of the AMS Volume 56, Number 2 Meetings & Conferences

Eduardo D. Sontag, Rutgers University, Title to be an- Special Sessions nounced. Algebraic Geometry (Code: SS 1A), Christopher Hacon, University of Utah, and Ziv Ran, University of California Special Sessions Riverside. Commutative Ring Theory (Code: SS 3A), Alan Loper, Fluid Mechanics (Code: SS 5A), James Kelliher and Qi Ohio State University, and Lee C. Klingler, Florida Atlantic Zhang, University of California Riverside. University. History and Philosophy of Mathematics (Code: SS 4A), Concentration, Functional Inequalities, and Isoperimetry Shawnee L. McMurran, California State University San (Code: SS 2A), Mario Milman, Florida Atlantic University, Bernardino, and James J. Tattersall, Providence College. Christian Houdre, Georgia Institute of Technology, and Noncommutative Geometry (Code: SS 2A), Vasiliy Emanuel Milman, Institute for Advanced Study. Dolgushev and Wee Liang Gan, University of California Constructive Mathematics (Code: SS 1A), Robert Lubar- Riverside. Representation Theory (Code: SS 3A), Vyjayanthi Chari, sky, Fred Richman, and Martin Solomon, Florida Atlantic Wee Liang Gan, and Jacob Greenstein, University of Cali- University. fornia Riverside. Enumerative Combinatorics (Code: SS 4A), Christian Krattenthaler, University of Vienna, and Aaron D. Mey- erowitz, Heinrich Niederhausen, and Wandi Wei, Florida Atlantic University. Seoul, Korea Harmonic Analysis (Code: SS 5A), Galia D. Dafni, Con- December 16–20, 2009 cordia University, and J. Michael Wilson, University of Wednesday – Sunday Vermont, Burlington. Meeting #1055 Associate secretary: Georgia Benkart Riverside, California Announcement issue of Notices: June 2009 Program first available on AMS website: Not applicable University of California Program issue of electronic Notices: Not applicable Issue of Abstracts: Not applicable November 7–8, 2009 Saturday – Sunday Deadlines For organizers: To be announced Meeting #1054 For consideration of contributed papers in Special Ses- Western Section sions: To be announced Associate secretary: Michel L. Lapidus For abstracts: To be announced Announcement issue of Notices: September 2009 Program first available on AMS website: September 24, 2009 San Francisco, Program issue of electronic Notices: November 2009 Issue of Abstracts: Volume 30, Issue 4 California Deadlines Moscone Center West and the San Fran- For organizers: April 6, 2009 cisco Marriott For consideration of contributed papers in Special Ses- sions: July 21, 2009 January 13–16, 2010 For abstracts: September 15, 2009 Wednesday – Saturday Joint Mathematics Meetings, including the 116th Annual The scientific information listed below may be dated. Meeting of the AMS, 93rd Annual Meeting of the Math- ematical Association of America (MAA), annual meetings For the latest information, see www.ams.org/amsmtgs/ of the Association for Women in Mathematics (AWM) and sectional.html. the National Association of Mathematicians (NAM), and the Invited Addresses winter meeting of the Association for Symbolic Logic (ASL), with sessions contributed by the Society of Industrial and Christopher Hacon, University of Utah, Title to be an- Applied Mathematics (SIAM). nounced. Associate secretary: Matthew Miller Birge Huisgen-Zimmerman, University of California Announcement issue of Notices: October 2009 Santa Barbara, Title to be announced. Program first available on AMS website: November 1, Jun Li, Stanford University, Title to be announced. 2009 Joseph Teran, University of California Los Angeles, Program issue of electronic Notices: January 2010 Title to be announced. Issue of Abstracts: Volume 31, Issue 1

February 2009 Notices of the AMS 331 Meetings & Conferences

Deadlines For organizers: April 1, 2009 Albuquerque, New For consideration of contributed papers in Special Ses- sions: To be announced Mexico For abstracts: To be announced University of New Mexico April 17–18, 2010 Lexington, Kentucky Saturday – Sunday University of Kentucky Western Section Associate secretary: Michel L. Lapidus March 27–28, 2010 Announcement issue of Notices: To be announced Saturday – Sunday Program first available on AMS website: To be an- Southeastern Section nounced Associate secretary: Matthew Miller Program issue of electronic Notices: To be announced Announcement issue of Notices: To be announced Issue of Abstracts: To be announced Program first available on AMS website: To be an- Deadlines nounced For organizers: September 17, 2009 Program issue of electronic Notices: To be announced For consideration of contributed papers in Special Ses- Issue of Abstracts: To be announced sions: To be announced Deadlines For abstracts: To be announced For organizers: August 28, 2009 For consideration of contributed papers in Special Ses- sions: To be announced Hoboken, New Jersey For abstracts: To be announced New Jersey Institute of Technology May 22–23, 2010 St. Paul, Minnesota Saturday – Sunday Eastern Section Macalester College Associate secretary: Steven H. Weintraub Announcement issue of Notices: To be announced April 10–11, 2010 Program first available on AMS website: To be an- Saturday – Sunday nounced Central Section Program issue of electronic Notices: To be announced Associate secretary: Susan J. Friedlander Issue of Abstracts: To be announced Announcement issue of Notices: To be announced Program first available on AMS website: To be an- Deadlines nounced For organizers: November 23, 2009 Program issue of electronic Notices: To be announced For consideration of contributed papers in Special Ses- Issue of Abstracts: To be announced sions: To be announced For abstracts: To be announced Deadlines For organizers: September 10, 2009 For consideration of contributed papers in Special Ses- Berkeley, California sions: To be announced For abstracts: To be announced University of California Berkeley June 2–5, 2010 Wednesday – Saturday Eighth Joint International Meeting of the AMS and the Sociedad Matemática Mexicana. Associate secretary: Susan J. Friedlander Announcement issue of Notices: February 2010 Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced

332 Notices of the AMS Volume 56, Number 2 Meetings & Conferences

Deadlines For organizers: To be announced New Orleans, For consideration of contributed papers in Special Ses- sions: To be announced Louisiana For abstracts: To be announced New Orleans Marriott and Sheraton New Notre Dame, Indiana Orleans Hotel January 5–8, 2011 Notre Dame University Wednesday – Saturday September 18–19, 2010 Joint Mathematics Meetings, including the 117th Annual Saturday – Sunday Meeting of the AMS, 94th Annual Meeting of the Math- Central Section ematical Association of America, annual meetings of the Associate secretary: Susan J. Friedlander Association for Women in Mathematics (AWM) and the Announcement issue of Notices: To be announced National Association of Mathematicians (NAM), and the Program first available on AMS website: To be an- winter meeting of the Association for Symbolic Logic (ASL), nounced Program issue of electronic Notices: To be announced with sessions contributed by the Society for Industrial and Issue of Abstracts: To be announced Applied Mathematics (SIAM). Associate secretary: Steven H. Weintraub Deadlines Announcement issue of Notices: October 2010 For organizers: February 19, 2010 Program first available on AMS website: November 1, For consideration of contributed papers in Special Ses- 2010 sions: To be announced Program issue of electronic Notices: January 2011 For abstracts: To be announced Issue of Abstracts: Volume 32, Issue 1 Los Angeles, Deadlines For organizers: April 1, 2010 California For consideration of contributed papers in Special Ses- sions: To be announced University of California Los Angeles For abstracts: To be announced October 9–10, 2010 Saturday – Sunday Western Section Statesboro, Georgia Associate secretary: Michel L. Lapidus Georgia Southern University Announcement issue of Notices: To be announced Program first available on AMS website: To be an- March 12–13, 2011 nounced Saturday – Sunday Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Southeastern Section Associate secretary: Matthew Miller Deadlines Announcement issue of Notices: To be announced For organizers: March 10, 2010 Program first available on AMS website: To be an- For consideration of contributed papers in Special Ses- nounced sions: To be announced Program issue of electronic Notices: To be announced For abstracts: To be announced Issue of Abstracts: To be announced

Deadlines For organizers: August 12, 2010 For consideration of contributed papers in Special Ses- sions: To be announced For abstracts: To be announced

February 2009 Notices of the AMS 333 Meetings & Conferences Boston, Baltimore, Maryland Massachusetts Baltimore Convention Center John B. Hynes Veterans Memorial Conven- January 15–18, 2014 Wednesday – Saturday tion Center, Boston Marriott Hotel, and Joint Mathematics Meetings, including the 120th Annual Boston Sheraton Hotel Meeting of the AMS, 97th Annual Meeting of the Math- ematical Association of America, annual meetings of the January 4–7, 2012 Association for Women in Mathematics (AWM) and the Wednesday – Saturday National Association of Mathematicians (NAM), and the Joint Mathematics Meetings, including the 118th Annual winter meeting of the Association for Symbolic Logic, with Meeting of the AMS, 95th Annual Meeting of the Math- sessions contributed by the Society for Industrial and Ap- ematical Association of America, annual meetings of the plied Mathematics (SIAM). Association for Women in Mathematics (AWM) and the Associate secretary: Matthew Miller National Association of Mathematicians (NAM), and the Announcement issue of Notices: October 2013 winter meeting of the Association for Symbolic Logic (ASL), Program first available on AMS website: November 1, with sessions contributed by the Society for Industrial and 2013 Applied Mathematics (SIAM). Program issue of electronic Notices: January 2013 Associate secretary: Michel L. Lapidus Issue of Abstracts: Volume 35, Issue 1 Announcement issue of Notices: October 2011 Program first available on AMS website: November 1, Deadlines 2011 For organizers: April 1, 2013 Program issue of electronic Notices: January 2012 For consideration of contributed papers in Special Ses- Issue of Abstracts: Volume 33, Issue 1 sions: To be announced Deadlines For abstracts: To be announced For organizers: April 1, 2011 For consideration of contributed papers in Special Ses- sions: To be announced San Antonio, Texas For abstracts: To be announced Henry B. Gonzalez Convention Center and Grand Hyatt San Antonio San Diego, California January 10–13, 2015 San Diego Convention Center and San Saturday – Tuesday Diego Marriott Hotel and Marina Joint Mathematics Meetings, including the 121st Annual Meeting of the AMS, 98th Annual Meeting of the Math- January 9–12, 2013 ematical Association of America, annual meetings of the Wednesday – Saturday Association for Women in Mathematics (AWM) and the Joint Mathematics Meetings, including the 119th Annual National Association of Mathematicians (NAM), and the Meeting of the AMS, 96th Annual Meeting of the Math- winter meeting of the Association of Symbolic Logic, with ematical Association of America, annual meetings of the sessions contributed by the Society for Industrial and Ap- Association for Women in Mathematics (AWM) and the plied Mathematics (SIAM). National Association of Mathematicians (NAM), and the Associate secretary: Steven H. Weintraub winter meeting of the Association for Symbolic Logic (ASL), Announcement issue of Notices: October 2014 with sessions contributed by the Society for Industrial and Program first available on AMS website: To be an- Applied Mathematics (SIAM). nounced Associate secretary: Susan J. Friedlander Program issue of electronic Notices: January 2015 Announcement issue of Notices: October 2012 Issue of Abstracts: To be announced Program first available on AMS website: November 1, Deadlines 2012 Program issue of electronic Notices: January 2012 For organizers: April 1, 2014 Issue of Abstracts: Volume 34, Issue 1 For consideration of contributed papers in Special Ses- sions: To be announced Deadlines For abstracts: To be announced For organizers: April 1, 2012 For consideration of contributed papers in Special Ses- sions: To be announced For abstracts: To be announced

334 Notices of the AMS Volume 56, Number 2 Meetings and Conferences of the AMS

Associate Secretaries of the AMS NY 11201-2990; e-mail: [email protected]; telephone: Western Section: Michel L. Lapidus, Department of Math- 718-260-3505. Steven H. Weintraub (after January 31, 2009), ematics, University of California, Surge Bldg., Riverside, CA Department of Mathematics, Lehigh University, Bethlehem, 92521-0135; e-mail: [email protected]; telephone: PA 18105-3174; e-mail: [email protected]; tele- 951-827-5910. phone: 610-758-3717. Central Section: Susan J. Friedlander, Department of Math- Southeastern Section: Matthew Miller, Department of Math- ematics, University of Illinois at Chicago, 851 S. Morgan (M/C ematics, University of South Carolina, Columbia, SC 29208-0001, 249), Chicago, IL 60607-7045; e-mail: [email protected]; e-mail: [email protected]; telephone: 803-777-3690. telephone: 312-996-3041. 2009 Seoul, Korea Meeting: Georgia Benkart, University of Eastern Section: Lesley M. Sibner (until January 31, 2009), Wisconsin-Madison, Department of Mathematics, 480 Lincoln Department of Mathematics, Polytechnic University, Brooklyn, Drive, Madison, WI 53706-1388; e-mail: [email protected]. edu; telephone: 608-263-4283.

The Meetings and Conferences section of the Notices 2011 gives information on all AMS meetings and conferences January 5–8 New Orleans, Louisiana p. 333 approved by press time for this issue. Please refer to the page Annual Meeting numbers cited in the table of contents on this page for more March 12–13 Statesboro, Georgia p. 333 detailed information on each event. Invited Speakers and Special Sessions are listed as soon as they are approved by the 2012 cognizant program committee; the codes listed are needed January 4–7 Boston, Massachusetts p. 334 for electronic abstract submission. For some meetings the Annual Meeting list may be incomplete. Information in this issue may be 2013 dated. Up-to-date meeting and conference information can January 9–12 San Diego, California p. 334 be found at www.ams.org/meetings/. Annual Meeting 2014 Meetings: January 15–18 Baltimore, Maryland p. 334 2009 Annual Meeting March 27–29 Urbana, Illinois p. 322 2015 April 4–5 Raleigh, North Carolina p. 323 January 10–13 San Antonio, Texas p. 334 April 25–26 San Francisco, California p. 324 Annual Meeting April 25–26 Worcester, Massachusetts p. 326 October 16–18 Waco, Texas p. 329 Important Information Regarding AMS Meetings October 24–25 University Park, Pennsylvania p. 330 Potential organizers, speakers, and hosts should refer to page 89 in the January 2009 issue of the Notices for general October 30–Nov. 1 Boca Raton, Florida p. 330 information regarding participation in AMS meetings and November 7–8 Riverside, California p. 331 conferences. December 6–20 Seoul, Korea p. 331 Abstracts 2010 Speakers should submit abstracts on the easy-to-use interac- January 13–16 San Francisco, California p. 331 tive Web form. No knowledge of is necessary to submit Annual Meeting an electronic form, although those who use may submit March 27–28 Lexington, Kentucky p. 332 abstracts with such coding, and all math displays and simi- larily coded material (such as accent marks in text) must April 10–11 St. Paul, Minnesota p. 332 be typeset in . Visit http://www.ams.org/cgi-bin/ April 17–18 Albuquerque, New Mexico p. 332 abstracts/abstract.pl. Questions about abstracts may be May 22–23 Hoboken, New Jersey p. 332 sent to [email protected]. Close attention should be paid to June 2–5 Berkeley, California p. 332 specified deadlines in this issue. Unfortunately, late abstracts September 18–19 Notre Dame, Indiana p. 333 cannot be accommodated. October 9–10 Los Angeles, California p. 333

Conferences: (see http://www.ams.org/meetings/ for the most up-to-date information on these conferences.) Co-sponsored conferences: February 12–16, 2009: AAAS Meeting in Chicago, IL (see page 86, January 2009 issue for more information). June 13–July 3, 2009: Mathematics Research Communities, Snowbird, UT (see www.ams.org/amsmtgs/mrc.html for more information).

February 2009 Notices of the AMS 335 Stellar New Titles in Mathematics from Cambridge!

New in Paperback! 2nd New Title in a New Series! Statistical Models Edition Theory and Practice David Freedman The Perspectives in Logic series publishes substantial and high- $40.00: Pb: 978-0-521-74385-3: quality books whose central theme lies in some area or aspect of 420 pp. logic, particularly books that present new material not available in book form. The series ranges from introductory texts suitable The Monster Group for beginning graduate courses to specialized monographs at the and Majorana frontiers of research. Each book offers an illuminating perspective Involutions for its intended audience. A. A. Ivanov Cambridge Tracts in Subsystems of Second Order Arithmetic 2nd Mathematics Stephen G. Simpson Edition $99.00: Hb: 978-0-521-88994-0: $80.00: Hb: 978-0-521-88439-6: 460 pp. 300 pp.

Conceptual Mathematics Combinatorics: Analytic Number A First Introduction to Categories 2nd The Rota Way Theory Edition F. William Lawvere and Joseph P. S. Kung, Essays in Honour of Stephen H. Schanuel Gian-Carlo Rota, and Klaus Roth $140.00: Hb: 978-0-521-89485-2 Catherine H. Yan Edited by W. W. L. Chen, $60.00: Pb: 978-0-521-71916-2: Cambridge Mathematical W. T. Gowers, H. Halberstam, 408 pp. Library W. M. Schmidt, and $99.00: Hb: 978-0-521-88389-4 R. C. Vaughan A Compendium of $39.99: Pb: 978-0-521-73794-4: $120.00: Hb: 978-0-521-51538-2: 408 pp. Partial Differential 512 pp. Equation Models Analysis in Positive Method of Lines Analysis Characteristic Hilbert Transforms with Matlab Anatoly N. Kochubei Frederick W. King William E. Schiesser and Cambridge Tracts in Encyclopedia of Mathematics and its Graham W. Grifﬁ ths Mathematics Applications $99.00: Hb: 978-0-521-51986-1: Volume 1 $80.00: Hb: 978-0-521-50977-0: 400 pp. 225 pp. $150.00: Hb: 978-0-521-88762-5: 720 pp.

Numerical Solution How to Think Like a Hilbert Transforms Volume 2 of Hyperbolic Mathematician $150.00: Hb: 978-0-521-51720-1: 720 pp. Partial Differential A Companion to Undergraduate Mathematics Equations Hilbert Transforms Set Kevin Houston John A. Trangenstein $280.00: 2 Hb bks: 978-0-521-51723-2: 1,440 pp. $85.00: Hb: 978-0-521-89546-0 $80.00: Hb: 978-0-521-87727-5: $34.99: Pb: 978-0-521-71978-0: 616 pp. 282 pp.

Representation Trends in Stochastic Theorems in Analysis Hardy Spaces Edited by Jochen Blath, Javad Mashreghi Peter Mörters, and Michael Scheutzow London Mathematical Society Student Texts London Mathematical Society Lecture Note Series $120.00: Hb: 978-0-521-51768-3 $48.00: Pb: 978-0-521-73201-7: $76.00: Pb: 978-0-521-71821-9: 384 pp. 392 pp. Prices subject to change.

1-800-872-7423 www.cambridge.org/us/mathematics AMERICAN MATHEMATICAL SOCIETY A Selection of the Best-selling AMS Titles in 2008

Five-Minute A Course on the Web Graph Noncommutative Geometry, Mathematics Anthony Bonato, Ryerson University, Quantum Fields and Motives Ehrhard Behrends, Toronto, ON, Canada Alain Connes, Collège de France, Paris, Freie Universität Berlin, A solid mathematical introduction to France, and Matilde Marcolli, Max-Planck- Germany Internet mathematics, examining the Institut für Mathematik, Bonn, Germany Translated by David Kramer applications of graph theory to real- Significant detail on the interplay Engaging and enter- world networks between noncommutative geometry taining vignettes that This book is jointly published by the AMS and the and number theory, a tool in the Atlantic Association for Research in the Mathematical demonstrate how mathematics is Sciences (AARMS). exploration of space-time and the set of primes essential to understanding our every- Graduate Studies in Mathematics, Volume 89; 2008; day world 184 pages; Hardcover; ISBN: 978-0-8218-4467-0; This book is co-published with Hindustan Book Agency (New Delhi) 2008; 380 pages; Softcover; ISBN: 978-0-8218-4348-2; List US$45; AMS members US$36; Order code GSM/89 List US$35; AMS members US$28; Order code MBK/53 Colloquium Publications, Volume 55; 2008; 785 pages; Hardcover; ISBN: 978-0-8218-4210-2; List US$99; AMS Quantum Field Theory members US$79; Order code COLL/55 Ricci Flow and the Poincaré A Tourist Guide for Mathematicians Conjecture Gerald B. Folland, University of Higher Arithmetic John Morgan, Columbia University, New Washington, Seattle, WA An Algorithmic Introduction to Number York, NY, and Gang Tian, Princeton A world-class expositor’s presenta- Theory University, NJ, and Peking University, tion of the elements of quantum Beijing, China Harold M. Edwards, field theory in a form accessible to New York University, NY Full details of a complete proof of mathematicians An explanation of the important Poincaré Conjecture, Mathematical Surveys and Monographs, Volume 149; using geometric arguments present- number theory that 2008; 325 pages; Hardcover; ISBN: 978-0-8218-4705-3; gives the central role to deductive ed by Grigory Perelman List US$89; AMS members US$71; Order code SURV/149 reasoning, including algorithms and Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA). computational examples In Search of the Clay Mathematics Monographs, Volume 3; 2007; Student Mathematical Library, Volume 45; 2008; 521 pages; Hardcover; ISBN: 978-0-8218-4328-4; Riemann Zeros 210 pages; Softcover; ISBN: 978-0-8218-4439-7; List US$69; AMS members US$55; Order code CMIM/3 Strings, Fractal List US$39; AMS members US$31; Order code STML/45 Membranes and Noncommutative Stochastic Processes Spacetimes Geometry of Conics S. R. S. Varadhan, Courant Institute of Michel L. Lapidus, A. V. Akopyan and A. A. Zaslavsky, Mathematical Sciences, New York, NY University of California, CEMI RAN, Moscow, Russia Riverside, CA An introduction to stochastic A demonstration of the advantage processes from a leading contributor An unparalleled look at a new of purely geometric methods in the to probability theory approach to understanding the most study of conics Titles in this series are co-published with the Courant celebrated and daunting open prob- Mathematical World, Volume 26; 2007; 134 pages; Institute of Mathematical Sciences at New York lem in mathematics Softcover; ISBN: 978-0-8218-4323-9; List US$26; University. 2008; 558 pages; Hardcover; ISBN: 978-0-8218-4222-5; AMS members US$21; Order code MAWRLD/26 Courant Lecture Notes, Volume 16; 2007; 126 pages; List US$79; AMS members US$63; Order code MBK/51 Softcover; ISBN: 978-0-8218-4085-6; List US$29; AMS members US$23; Order code CLN/16

Contact the AMS: 1-800-321-4AMS (4267), in the U. S. and Canada, or 1-401-455-4000 (worldwide); fax:1-401-455-4046; email: [email protected]. American Mathematical Society, 201 Charles Street, Providence, RI 02904-2294 USA Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Quadratic Diophantine Multiscale Principles of Equations Finite Harmonic of the American Mathematical Society T. Andreescu, University of Texas at Element Analysis February 2009 Volume 56, Number 2 Dallas, Richardson, TX, USA; D. Andrica, Methods A. Deitmar, University Cluj-Napoca, Romania Theory and University of This text treats the classical theory of Applications Tübingen, quadratic diophantine equations and Germany; guides readers through the last two Y. Efendiev, Texas S. Echterhoff, decades of computational techniques A & M University, University of and progress in the area. The presenta- College Station, Texas, USA; T. Y. Hou, Münster, Germany California Institute of Technology, tion features two basic methods to This gently-paced book includes a full Pasadena, CA, USA investigate and motivate the study of proof of Pontryagin Duality and the quadratic diophantine equations: the This text on the main concepts and Plancherel Theorem. The authors theories of continued fractions and recent advances in multiscale finite emphasize Banach algebras as the quadratic fields. It also discusses Pell’s element methods is written for a broad cleanest way to get many fundamental Birds and Frogs equation. audience. Each chapter contains a results in harmonic analysis. simple introduction, a description of page 212 2009. Approx. 250 p. 20 illus. (Springer proposed methods, and numerical 2009. Approx. 345 p. (Universitext) Monographs in Mathematics) Softcover examples of those methods. Softcover ISBN 978-0-387-35156-8 ISBN 978-0-387-85468-7 $49.95 approx. $59.95 2009. X, 234 p. (Surveys and Tutorials in The Strong Free Will the Applied Mathematical Sciences) Solving Softcover Theorem Introduction to Siegel the Pell Modular Forms and ISBN: 978-0-387-09495-3 $44.95 Equation page 226 Dirichlet Series Intro M. J. Jacobson, Jr., A. Andrianov, Russian Academy of the duction to H. C. Williams, Sciences, Petersburg Department of the Boolean University of Steklov Institute of Mathematics, Calgary, AB, St. Petersburg, Russia Algebras Canada San Francisco This is intended for a graduate course S. Givant, Mills The authors provide a friendly Meeting on Siegel modular forms, Hecke College, Oakland, introduction to algebraic number operators, and related zeta functions. CA, USA; P. Halmos, theory via Pell’s Equation. The only page 324 The author’s aim is to present a concise deceased prerequisites are knowledge of and self-contained introduction to a This book is an informal though elementary number theory and abstract developing area of number theory that systematic series of lectures on Boolean algebra. Volume 56, Number 2, Pages 201–336, February 2009 will serve to attract young researchers algebras. It contains background Worcester Meeting to this field. chapters on topology and continuous 2009. Approx. 520 p. 20 illus. (CMS Books functions and includes hundreds of in Mathematics) Hardcover page 326 2009. XII, 184 p. (Universitext) Softcover exercises as well as a solutions manual. ISBN 978-0-387-84922-5 $79.95 ISBN 978-0-387-78752-7 $59.95 2009. XIV, 574 p. 10 illus. (Undergraduate Texts in Mathematics) Hardcover ISBN 978-0-387-40293-2 $59.95

Learn about our eBook Collection in Mathematics and Statistics. Talk to your Librarian Today

Trim: 8.25" x 10.75" 136 pages on 40 lb Cougar Opaque • Spine: 3/16" • Print Cover on 9pt Carolina