EMS Prizes

Felix Klein Prize

Ferran Sunyer i Balaguer Prize

The EMS prizes were established by the European Mathematical Society. They are meant to recognize excellent contributions in Mathematics by young researchers not older than 32 years. The prizes are presented every four years at the European Congresses of Mathematics.

The prize committee is appointed by the EMS. It consits of about fifteen internationally recognized mathematicians covering a large variety of fields. The first prize award was in Paris in 1992, the second in Budapest in 1996. The EMS prizes award will be presented at the 3ecm, carrying a monetary award of 6,000 Euro.

**Prize Committee**

Noga Alon (Tel Aviv)

Werner Ballmann (Bonn)

Jan Derezinski (Warsawa)

Maxim Kontsevich (Bures-sur-Yvette)

Eduard Looijenga (Utrecht)

Angus Macintyre (Edinburgh)

David Nualart (Barcelona)

Aleksei Parshin (Moscow)

Ragni Piene (Oslo)

Itamar Procaccia (Tel Aviv)

Mario Pulvirenti (Roma)

Rolf Rannacher (Heidelberg)

Caroline Series (Warwick)

Vladimir Sverák (Praha)

Dan Voiculescu (Berkeley)

**Semyon Alesker** (Israel)

Semyon Alesker contributed greatly both to the Asymptotic Theory of Convexity and to Classical Convexity Theory. His most significant work is on valuations (additive functionals) on convex bodies and it has remodeled a central part of convex geometry.

Group invariant valuations were studied since Dehn's solution of Hilbert's third problem, with later contributions by Blaschke and others, and culminating in Hadwiger's celebrated characterization theory for the intrinsic volumes. The latter theorem was considered the top result in this area for almost fifty years. Alesker has now considerably extended this theory, obtaining very complete classification results under weaker invariance assumptions. He approximated (continuous) rotation invariant valuations by polynomial valuations and characterized the latter, making use of representations of the orthogonal group. This enabled him to extend Hadwiger's theorem to tensor valued valuations. In another direction, he solved a problem of McMullen, in a much stronger form, showing that translation invariant valuations are essentially (up to linear combinations and approximation) mixed volumes. The approach is via representation theory of the general linear group and involves a surprising application of D-modules. The new approach has also opened the way to finiteness results for valuations with other group invariances.

**Raphael Cerf** (France)

Raphael Cerf became known through his results on Probability theory. Using a large deviation principle in the proper topology, Raphael Cerf has established a Wulff construction for the supercritical percolation model in three dimensions. This reslut is a very major advance in the subject, and provides the right formulation for the geometry of the problem. Raphael Cerf has been able to carry out this program using a correct mixture of combinatorial arguments, geometric ideas and probabilistic tools.

In addition to this research, Raphael Cerf has made original contributions in genetic algorithms. He has solved a central problem in bootstrap percolation and extended to three dimensions the metastable behavior of the stochastic Ising model in the limit of low temperatures.

**Dennis Gaitsgory** (USA)

Dennis Gaitsgory is one of the leaders in the geometric Langlands correspondence and related areas. In the modern ``geometric'' representation theory one replaces functions by complexes of constructible sheaves on (infinite-dimensional) algebraic varieties. In this way many deep structures appear, and classical results in the theory of automorphic forms can be seen much more clearly.

In his thesis and in the subsequent work with Braverman, Gaitsgory established fundamental properties of Eisenstein series in the geometric setting. In a recent paper on nearby cycles, he proposed an extremely elegant construction of the convolution of equivariant perverse sheaves on so-called affine Grassmannians. This implies that the center of the affine Hecke algebra conincides with the whole spherical Hecke algebra. Also, it gives the best conceptual explanation of the Satake equivalence.

Recent work of Gaitsgory relates finite quantum groups and chiral Hecke algebras. It is a very important step in the program of Beilinson and Drienfield in the geometric Landlands theory.

**Emmanuel Grenier** (France)

Emmanuel Grenier greatly contibuted to the asymptotic analysis of Euler and Navier-Stokes equations with large Coriolis force. The simplest case (when the equations are set on the unit cube with periodic boundary conditions) has been solved by Grenier around 1995. Later, in collaboration with Desjardins, Dormy, and Masmoudi, he gave rigorous derivations of several asymptotic models currently used in Ocean and Atmosphere modeling, or in Magnetohydrodynamics.

Grenier obtained both positive and negative important results on the problem of convergence of the Navier-Stokes equations to the Euler equations in a domain with solid boundary conditions. In particular, he showed that the positive results of Caflisch and Sammartino obtained for analytic initial data, cannot be extended to Sobolev data. He also justified the hydrostatic limit of the Euler equations in a two dimensional infinitesimally thin strip.

Grenier gave a very elegant proof of convergence for the semi-classical limit of the nonlinear Schroedinger equations (before appearance of shocks). He also obtained, simultaneously with E. Rykow and Sinai, a hydrodynamic limit for Zelodvich adhesion particle model.

**Dominic Joyce** (U.K.)

Dominic Joyce's work on the existence of metrics with special holomony is among the best in Riemannian geometry in the last decade. The question of the existence of Riemannian metrics with special holomony has a long history beginning with the work of Cartan. It includes some of the best work of such people as M. Berger, J. Simons, S.T. Yau and B. Bryant. Using a dazzling display of geometry and analysis, Joyce constructed compact examples in the exceptional cases where the holonomy is Spin7 and G2 the only remaining possibilities, the others on Berger's list had been eliminated. Joyce also computed the dimension of the deformation spaces of such metrics and many other of their invariants. As a result, he also discovered a totally unexpected version of mirror symmetry for such spaces. Dominic Joyce is one of the leading young differential geometers.

**Vincent Lafforgue** (France)

Vincent Lafforgue's work is a major advance in the K-theory of operator algebras: the proof of the Baum-Connes conjecture for discrete co-compact subgroups of SL3(R), SL3(C), SL3(Qp) and some other locally compact group (and of more general objects). The conjecture plays a central role in non-commutative geometry and has far-reaching connections to the Novikov conjecture on higher signatures in topology, to harmonic analysis on discrete groups and the theory of C*-algebras. Lafforgue's result is the first passage of the barrier which property T of Kazhdan has posed for many years in the proof of the Baum-Connes conjecture. The proof involves several remarkable technical and conceptual developments, like a bivariant K-theory for Banach algebras (versus Kasparov's by now classical one for C*-algebras) or establishing the conjecture for various completions of the L1 algebras of the groups.

**Michael McQuillan** (U.K.)

Michael McQuillan has created the method of dynamic diophantine approximation which has led to a series of remarkable results in complex geometry of algebraic varieties. Among these results one can mention a new proof of Bloch's conjecture on holomorphic curves in closed subvarieties of abelian varieties, the proof of the conjecture of Green and Griffiths that a holomorphic curve in a surface of general type cannot be Zariski-dense, and the hyperbolicity for generic hypersurfaces in a projective space P3 of high enough degree (Kobayashi conjecture).

**Stefan Yu. Nemirovski** (Russia)

S.Yu. Nemirovski has obtained several strong results on topology and complex analysis. Using modern techniques like the famous Seiberg-Witten invariants he has solved some old classical problems about sub-manifolds in complex domains. First, he generalized Thom inequality proved by P. Kronheimer and T. Mrowka. As a very particular case he proved that there are no nonconstant holomorphic functions in a neighbourhood of an embedded non-trivial 2-sphere in a complex projective plane. Another application of his main theorems is also very attractive. Suppose that an analytic disc is attached from the outside to a strictly pseudoconvex domain U in a complex 2-plane, then there is no smooth disc inside of U wich the same boundary. As a corollary one gets that it is impossible to attach an analytic disc from the outside to a strictly pseudoconvex domain that is diffeomorphic to a closed ball.

**Paul Seidel** (France)

Paul Seidel became known through his work on symplectic topology. In his PhD theses he studied the fundamental question whether symplectic diffeomorphisms which are diffeotopic to the identity are also symplectically diffeotopic to the identity. He showed that the answer is negative in many cases, already in dimension 4. His counterexamples are generalized Dehn twists, his proof involves Floer homology. In further works, Seidel constructed a natural representation of the fundamental group of the group of Hamiltonian symplectomorphisms into the quantum cohomology ring. This work was basic for later work of Lalonde, McDuff, and Polterovich on the topology of the group of symplectomorphisms. There is more to say about other work. His latest work is related to mirror symmetry, showing his broad horizon.

**Wendelin Werner** (France)

Wendelin Werner has obtained deep results on stochastic processes and, more precisely, he has proved a number of significant results on Brownian path properties, including the shape of Brownian islands and Brownian windings.

Wendelin Werner has made remarkable contributions to the study of self-avoinding random walks and the corresponding critical exponents. More specifically, he obtained the first non-trivial upper bound of the disconnection exponent, and he developed an elegant approach for studying the limiting behavior of the non-intersection exponents for a great number of independent Brownian motions. Among many other interesting works he constructed, with a collaborator, the so-called true self-repelling motion using an ingenious method involvin infinite systems of coalescing Brownian motions.

The Felix Klein prize has been established by the European Mathematical Society and the endowing organisation, the Institute for Industrial Mathematics in Kaiserslautern. It is awarded to a young scientist or a small group of young scientists (normally under the age of 38) for using sophisticated methods to give an outstanding solution, which meets with the complete satisfaction of industry, to a concrete and difficult industrial problem. The prize is presented every four years at the European Congresses of Mathematics. The prize committee consists of six members appointed by agreement of the EMS and the Institute for Industrial Mathematics in Kaiserslautern. The first prize will be presented at the 3ecm. It carries a monetary award of 5,000 Euro.

**Prize Committee**

Heinz Engl (Linz)

Andreas Frank (Budapest)

Horst Loch (Mainz)

Olivier Pironneau (Paris)

John Ockendon (Oxford)

**David C. Dobson** (U.S.A.)

David C. Dobson started his work on the diffraction of electromagnetic waves from periodic structures, when he was a postdoc at the famous Institute of Mathematics and its Applications of Professor Avner Friedman. The Honeywell Technology Center had posed the problem to model and analyse the diffraction and to develop appropriate numerical algorithms. In a next step an optimal shape design problem for phase lenses was solved. The fact that he used a ``Fraunhofer approximation'' was not(!) the reason to give him a prize endowed by the Fraunhofer Institute for Mathematics; what convinced the committee that he should be the first prize winner was that he used rigorous and sound mathematical methods in a quite tricky way for a problem which Honeywell states to be of very high industrial importance.

Ferran Sunyer i Balaguer (1912-1967) was a self-taught Catalan mathematician who, in spite of a serious physical disability, was very active in research in classical Mathematical Analysis, an area in which he acquired international recognition. Each year in honour of the memory of Ferran Sunyer i Balaguer, the Institut d'Estudis Catalans awards an international mathematical research prize bearing his name, open to all mathematicians. This prize was awarded for the first time in April 1993. For further information on the Ferran Sunyer i Balaguer Foundation, see http://crm.es/info/ffsb.htm.

**Prize Committee**

Pilar Bayer (Barcelona)

Antonio Córdoba (Madrid)

Paul Malliavin (Paris)

Alan Weinstein (Berkeley)

**Juan-Pablo Ortega** (Spain), **Tudor Ratiu** (Romania)

The Institut d'Estudis Catalans has awarded the 1999 Ferran Sunyer i Balaguer Prize to Professors Juan-Pablo Ortega and Tudor Ratiu for their monograph entitled Hamiltonian Singular Reduction.

The awarded monograph deals with the reduction of Hamiltonian systems using its symmetries. In the case of smooth systems there is a standard formulation of this procedure due to Marsden and Weinstein. In the presence of singularities, several approaches exist to the reduction procedure. The main contribution of the authors is to show that all these approaches are in some sense equivalent by giving a sort of universal model for singular reduction. The monograph is self-contained and will be of great use to researchers in this area.

Professor Tudor Ratiu, professor at the École Polytechnique Fédérale de Lausanne, is a well-known specialist in the field. Professor Juan-Pablo Ortega completed in 1998 a Ph.D. thesis in the area at the University of California at Santa Cruz and he is presently at the École Polytechnique Fédérale de Lausanne as well.