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Mathematics People, Volume 51, Number 9

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Mathematics People, Volume 51, Number 9 Mathematics People contributions is his surprising solution of the symplectic Prizes Presented at the packing problem, completing work of Gromov, McDuff, and Polterovich, showing that compact symplectic manifolds European Congress of can be packed by symplectic images of equally sized Eu- Mathematicians clidean balls without wasting volume if the number of balls is not too small. Among the corollaries of his proof, The European Mathematical Society (EMS) awarded a num- Biràn obtains new estimates in the Nagata problem. A ber of prizes at the 2004 European Congress of Mathe- powerful tool in symplectic topology is Biràn’s decompo- maticians, held in Stockholm, Sweden, 27 June–2 July, sition of symplectic manifolds into a disc bundle over a 2004. The EMS prizes are awarded every four years in con- symplectic submanifold and a Lagrangian skeleton. Ap- junction with the congress in recognition of distinguished plications of this discovery range from the phenomenon contributions in mathematics by young researchers not of Lagrangian barriers to surprising novel results on topol- older than 35 years. The prize carries a cash value of 5,000 ogy of Lagrangian submanifolds. Paul Biràn not only proves euros (about US$6,000). The names of the awardees, their deep results, he also discovers new phenomena and invents institutions, and brief descriptions of their work follow. powerful techniques important for the future develop- FRANCK BARTHE, the Institut de Mathématiques Labora- ment of the field of symplectic geometry. toire de Statistique et Probabilités, Toulouse, France: Barthe ELON LINDENSTRAUSS, Clay Mathematics Institute and pioneered the use of measure-transportation techniques Courant Institute of Mathematical Sciences, USA: Elon Lin- (due to Kantorovich, Brenier, Caffarelli, McCann, and oth- destrauss has done deep and highly original work at the ers) in geometric inequalities of harmonic and functional interface of ergodic theory and number theory. Although analysis with striking applications to geometry of convex he has worked widely in ergodic theory, his recent proof bodies. His major achievement is an inverse form of clas- of the quantum unique ergodicity conjecture for arith- sical Brascamp-Lieb inequalities. Further contributions in- metic hyperbolic surfaces breaks fertile new ground, with clude discovery of a functional form of isoperimetric in- great promise for future applications to number theory. equalities and a recent solution (with Artstein, Ball, and Already, in joint work with Katok and Einsiedler, he has Naor) of a long-standing Shannon’s problem on entropy used some of the ideas in this work to prove the celebrated production in random systems. conjecture of Littlewood on simultaneous diophantine ap- STEFANO BIANCHINI, the Instituto per le Applicazioni del proximation for all pairs of real numbers lying outside a Calcolo “M. Picone”, Rome, Italy: Stefano Bianchini has in- set of Hausdorff dimension zero. This goes far beyond what troduced an entirely new perspective to the theory of dis- was known earlier about Littlewood’s conjecture and spec- continuous solutions of one-dimensional hyperbolic con- tacularly confirms the high promise of the methods of er- servation laws, representing solutions as local godic theory in studying previously intractable problems superposition of traveling waves and introducing innova- of diophantine approximation. tive Glimm functionals. His ideas have led to the solution ANDREI OKOUNKOV, Princeton University, USA: Andrei Ok- of the long-standing problem of stability and convergence ounkov contributed greatly to the field of asymptotic com- of vanishing viscosity approximations. In his best individual binatorics. An extremely versatile mathematician, he found achievement, published in 2003 in Arch. Rational Mech. a wide array of applications of his methods. His early re- Anal., he shows convergence of semidiscrete upwind sults include a proof of a conjecture of Olshanski on the schemes for general hyperbolic systems. In the techni- representation theory of groups with infinite-dimensional cally demanding proof the traveling waves are constructed duals. Okounkov gave the first proof of the celebrated as solutions of a functional equation, applying center man- Baik-Deift-Johansson conjecture, which states that the as- ifold theory in an infinite-dimensional space. ymptotics of random partitions distributed according to the PAUL BIRÀN, Tel-Aviv University, Israel: Paul Biràn has Plancherel measure coincides with that of the eigenvalues made fundamental and influential contributions to sym- of large Hermitian matrices. An important and influential plectic topology as well as to algebraic geometry and result of Okounkov is a formula he found in joint work with Hamiltonian systems. His work is characterized by new Borodin, which expresses a general Toeplitz determinant depths in the interactions between complex algebraic as the Fredholm determinant of the product of two asso- geometry and symplectic topology. One of the earlier ciated Hankel operators. The new techniques of working 1070 NOTICES OF THE AMS VOLUME 51, NUMBER 9 Mathematics People with random partitions invented and successfully devel- mysterious relations between exact arithmetic formulae oped by Okounkov lead to a striking array of applications and special values of L-functions, as typified by the con- in a wide variety of fields: topology of moduli spaces, er- jecture of Birch and Swinnerton-Dyer. Venjakob’s work ap- godic theory, the theory of random surfaces, and algebraic plies quite generally to towers of number fields whose Ga- geometry. lois group is an arbitrary compact p-adic Lie group (which SYLVIA SERFATY, the Courant Institute of Mathematical Sci- is not, in general, commutative) and has done much to show ences, USA: Sylvia Serfaty was the first to make a system- that a rich theory is waiting to be developed. His most im- atic and impressive asymptotic analysis for the case of large portant results include the proof of a good dimension parameters in theory of the Ginzburg-Landau equation. She theory for modules over Iwasawa algebras and the proof established precisely the values of the first, second, and of the first case of a structure theory for modules over these third (with E. Sandier) critical fields for nucleation of one algebras. With Hachimori he discovered the first examples stable vortex, vortex fluids, and surface superconductiv- of arithmetic Iwasawa modules which are completely faith- ity. In micromagnetics, her work with F. Alouges and T. Riv- ful, as well as proving a remarkable asymptotic upper ière breaks new ground on singularly perturbed varia- bound for the rank of the Mordell Weil group of elliptic tional problems and provides the first explanation for the internal structure of cross-tie walls. curves in certain towers of number fields over Q whose Galois group is a p-adic Lie group of dimension 2. Very re- STANISLAV SMIRNOV, Royal Institute of Technology, Swe- den, and University of Geneva, Switzerland: Stanislav cently, he found the key to the problem of defining, in non- Smirnov’s most striking result is the proof of existence and commutative Iwasawa theory, the analogue of the char- conformal invariance of the scaling limit of crossing prob- acteristic series of modules over Iwasawa algebras. abilities for critical percolation on the triangular lattice. The Carl-Erik Fröberg Prize was also awarded at the ECM. This gives a formula for the limiting values of crossing The prize is awarded in even-numbered years to a young probabilities, a breakthrough in the field, which has allowed Nordic author of an article published in the journal BIT Nu- for the verification of many conjectures of physicists con- merical Mathematics. The prize was awarded to ANNA- cerning power laws and critical values of exponents. KARIN TORNBERG of the Courant Institute of Mathematical Stanislav Smirnov also made several essential contributions Sciences for her article “Multidimensional quadrature of to complex dynamics around the geometry of Julia sets and singular and discontinuous functions”. The prize carries the thermodynamic formalism. a cash award of SEK 30,000 (about US$4,000). XAVIER TOLSA, ICREA and the Universitat Autònoma de Barcelona, Spain: Xavier Tolsa has made fundamental con- —From an ECM announcement tributions to harmonic and complex analysis. His most out- standing work solves Vitushkin’s problem about semiad- ditivity of analytic capacity. The problem was raised in 1967 by Vitushkin in his famous paper on rational approxima- Serguei Denissov Awarded tion in the plane. Tolsa’s result has important conse- Popov Prize quences for a classical (100 years old) problem of Painlevé about a geometric characterization of planar compact sets SERGUEI DENISSOV of the California Institute of Technology that are removable in the class of bounded analytic func- was awarded the fourth Vasil Popov Prize at the Interna- tions. Answering affirmatively Melnikov’s conjecture, Tolsa tional Conference in Approximation Theory held in Gatlin- provides a solution of the Painlevé problem in terms of the burg, Tennessee, in May 2004. The Popov Prize is awarded Menger curvature. Xavier Tolsa has also published many every third year to a young mathematician (within six important and influential results related to Calderón- years of receipt of the Ph.D.) who has made outstanding Zygmund theory and rational approximation in the plane. research contributions to approximation theory and related WARWICK TUCKER, Uppsala
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