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ISSN 0002-9920 of the American Mathematical Society February 2006 Volume 53, Number 2 Math Circles and Olympiads MSRI Asks: Is the U.S. Coming of Age? page 200 A System of Axioms of Set Theory for the Rationalists page 206 Durham Meeting page 299 San Francisco Meeting page 302 ICM Madrid 2006 (see page 213) > To mak• an antmat•d tub• plot Animated Tube Plot 1 Type an expression in one or :;)~~~G~~~t;~~i~~~~~~~~~~~~~:rtwo ' 2 Wrth the insertion point in the 3 Open the Plot Properties dialog the same variables Tl'le next animation shows • knot Plot 30 Animated + Tube Scientific Word ... version 5.5 Scientific Word"' offers the same features as Scientific WorkPlace, without the computer algebra system. Editors INTERNATIONAL Morris Weisfeld Editor-in-Chief Enrico Arbarello MATHEMATICS Joseph Bernstein Enrico Bombieri Richard E. Borcherds Alexei Borodin RESEARCH PAPERS Jean Bourgain Marc Burger James W. Cogdell http://www.hindawi.com/journals/imrp/ Tobias Colding Corrado De Concini IMRP provides very fast publication of lengthy research articles of high current interest in Percy Deift all areas of mathematics. All articles are fully refereed and are judged by their contribution Robbert Dijkgraaf to the advancement of the state of the science of mathematics. Issues are published as S. K. Donaldson frequently as necessary. Each issue will contain only one article. IMRP is expected to publish 400± pages in 2006. Yakov Eliashberg Edward Frenkel Articles of at least 50 pages are welcome and all articles are refereed and judged for Emmanuel Hebey correctness, interest, originality, depth, and applicability. Submissions are made by e-mail to Dennis Hejhal [email protected]. An abstract for each article should be included. A copy may also Helmut Hofer be sent to an editor. Only an acknowledgment from the editorial office officially establishes Gerhard Huisken the date of receipt. Submissions not prepared using TeX should be typed or printed on one Yasutaka Ihara side of the page, be double-spaced (including references), and have ample margins. Check Michio Jimbo contact information for submission by fax or post. When articles are accepted, production Kurt Johansson begins immediately; authors should be available to assist the editorial staff. Masaki Kashiwara Please note that it is a condition of submission of a paper that the author(s) permit editing Kiran S. Kedlaya the paper for language correctness, readability, and compliance with the IMRP mathematical Carlos Kenig style. Sergiu Klainerman Illustrations can be in color. There are no page charges. Each author shall receive 100 Toshiyuki Kobayashi complimentary reprints with covers. Maxim Kontsevich Igor Krichever Recently Published Articles Shigeo Kusuoka Gilles Lebeau • Degasperis-Procesi Peakons and the Discrete Cubic String, Joachim Lohkamp Hans Lundmark and Jacek Szmigielski John Lott • Mckay's Observation and Vertex Operator Algebras Generated by Tvvo Conformal Vectors Nikolai Makarov of Central Charge 1/2, Ching Hung Lam, Hiromichi Yamada, and Hiroshi Yamauchi Yu. I. Manin • Graded Multiplicities in the Macdonald Kernel. Part I, John R. Stembridge Barry Mazur Haynes Miller • Bost-Connes-Marcolli Systems for Shimura Varieties. Part I. Definitions and Formal Shinichi Mochizuki Analytic Properties, Eugene Ha and Frederic Paugam Fabien Morel • The Ci-Approach to Approximate Inverse Scattering at Fixed Eric Opdam Energy in Three Dimensions, R . G. Novikov Michael Rapoport • The Blowup Behavior of the Biharmonic Map Heat Flow N. Yu. Reshetikhin in Four Dimensions, Roger Moser Igor Rodnianski Peter Sarnak Subscription Information Freydoon Shahidi Stanislav Smirnov Subscription E-mail: [email protected] Michael Struwe Institutional subscription rates for 2006 (400± pages) are $195.00 for online only, $214.50 G. Tian for print only, and $234.00 for both online and print editions. Subscribers to the online John Toth only edition or to the print and online editions of the journal in 2006 will get perpetual Takeshi Tsuji access to volumes 2005-2006 (i.e., permanent online access to volumes 2005-2006 even if the David Vogan subscription is canceled in the future). Dan-Virgil Voiculescu All orders should be accompanied by payment and sent to Hindawi Publishing Corporation, Andrei Zelevinsky 410 Park Avenue, 15th Floor, #287 pmb, New York, NY 10022, USA. Maciej Zworski W JN 07\WJ Hindawi Publishing Corporation, 410 Park Avenue, 15th Floor, #287 pmb, New York, NY 10022, USA; II A Fax: 1 866-446 3294 (USA, toll-free); URL: http://www.hindawi.com; E mail: hindawi@hindawi com NEW (6 NOTEWORTHY from Birkhiiuser ToRies in the Theory of Vortices in Bose-Einstein Introduction to Plane Alg:ebraic Function Fields Condensates Algebraic Curves GABRIEL DANIEL VILLA SALVADOR, C/NVESTAV del lPN, AMANDINE AFTALION, CNRS, Laboratoire Jacques-Louis ERNST KUNZ, University of Regensburg, Germany MexicOCity, Mexico Lions, Paris, France RICHARD G. BELSHOFF, Southwest Missouri State University, Springfield, MO (Translator) Algebraic function fields of one variable are used in One of the key issues related to superfluidity is the This work treats an introduction to commutat several areas of mathematics: complex analysis, existence of vortices. In very recent experiments on ive ring theory and algebraic plane curves, algebraic geometry, and number theory. This text Bose- Einstein condensates, vortices have been requiring of the student only a basic knowledge of algebra, applies an arithmetic-algebraic viewpoint to the study of observed in various conditions. This monograph is with all of the algebraic facts collected into severa function fields as part of the algebraic theory of dedicated to the mathematical modeling of these l appendices that can be easily referre numbbrs. The author does not ignore the geometric and phenomena. The mathematical tools employed are d to, as needed. Kunz's proven conception of teaching topics analytic aspects of function fields, but focuses on an in­ energy estimates, Gamma convergence, and in commutative algebra together with their applications to algebra depth examination from a number-theoretic perspec­ homogenization techniques. The mathematical analysis ic geometry makes this book tive. The exposition explains both the similarities and is made in the framework of the Gross- Pitaevskii significantly different from others on plane algebraic curves. fundamental differences between function fields and energy. Results are presented and open problems number fi elds, including many examples to motivate related to recent experiments are explained. From a review of the German edition: "The reader unde~standing and further study. The only prerequisites is invited to learn some topics from commutative ring are abasic knowledge of field theory, complex analysis, 2006/APPROX. 160 PP., 2S ILLUS./HARDCOVER theory by mainly studying their illustrations and and some commutative algebra. ISBN 0-8176-4392-3/$79.95 (TENT.) applications in plane curve theory. ... The whole text is a PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS real masterpiece of clarity, rigor, comprehension, The book can serve as a text for a graduate course in AND THEIR APPLICATIONS methodical skill, algebraic and geometric motivation .. number theory or an advanced graduate topics course. highly enlightening, motivating and entertaining at the Alternatively, chapters 1-4 can serve as the base of an same time. .. One simply cannot do better in writing introductory undergraduate course for mathematics Conformal Groups in Geometry such a textbook. " - ZENTRALBLATT MATH majors, while chapters 5-10 can support a second and Spin Structures course for advanced undergraduates. Researchers 2005/293 PP., 52 ILLUS./SOFTCOVER PIERRE ANGLES, Universite Paul Saba tier, Toulouse, France interested in number theory, fi eld theory, and their ISBN 0-81 76-4381-8/$59.95 interJctions will also find the work an excellent Conformal groups play a key role in geometry and spin reference. structures. This book provides a self-contained Compactifications of overview of this important area of mathematical physics, 2006/APPROX. 685 PP., 20 ILLUS./HARDCOVER beginning with its origins in the works of Cartan and Symmetric and Locally ISBN 0-8176-4480-6/$69.95 (TENT.) Chevalley and progressing to recent research in spinors Symmetric Spaces and conformal geometry. All the major aspects of the A. BOREL; LIZHEN JI, University of Michigan, field are introduced, followed by detailed descriptions Ann Arbor, Ml and definitions. Rich in exercises- accompanied by full Noncompact symmetric and locally symmetric spaces Vortices in the Magnetic proofs and hints,--the book will provide further naturally appear in many mathematical theories, directions for study and research. including analysis (representation theory, nonabelian Ginzburg-Landau Model harmonic analysis), number theory (automorphic ETIENNE SANDIER, Universite Paris-12 Val-de-Marne, 2006/APPROX. 320 PP., 40 ILLUS./HARDCOVER forms), algebraic geometry (modulae) and algebraic Creteil, France; SYLVIA SERFATY, CMLA, Ecole Normale ISBN 0-8176-3512-2/$89.95 (TENT.) topology (cohomology of discrete groups). ln most Superieure de Cachan, France PROGRESS IN MATHEMATICAL PHYSICS applications it is necessary to form an appropriate The Ginzburg-Landau (G- L) functional has become an compactification of the space. The literature dealing important phenomenological model since its Introduction to Complex with such compactifications is vast. The main purpose of confirmation both theoretically and experimentally.
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