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 has been presented in Barcelona in 2000. It carried a monetary award of 5,000 Euro.

2004

Franck Barthe, Institut de Mathématiques Laboratoire de Statistique et Probabilités, Toulouse, France

Barthe pioneered the use of measure-transportation techniques (due to Kantorovich, Brenier, Caffarelli, Mc Cann and others) in geometric inequalities of harmonic and functional analysis with striking applications to geometry of convex bodies. His major achievement is an inverse form of classical Brascamp-Lieb inequalities. Further contributions include discovery of a functional form of isoperimetric inequalities and a recent solution (with Artstein, Ball and Naor) of a long-standing Shannon's problem on entropy production in random systems.

Stefano Bianchini, Instituto per le Applicazioni del Calcolo "M. Picone", Rome, Italy

Stefano Bianchini has introduced an entirely new perspective to the theory of discontinuous solutions of one-dimensional hyperbolic conservation laws, representing solutions as local superposition of travelling waves and introducing innovative Glimm functionals. His ideas have led to the solution of the long standing problem of stability and convergence of vanishing viscosity approximations. In his best individual achievement, published in 2003 in Arch.Ration. Mech. Anal., he shows convergence of semidiscrete upwind schemes for general hyperbolic systems. In the technically demanding proof the travelling waves are constructed as solutions of a functional equation, appling center manifold theory in an infinite dimensional space.

Paul Biràn, School of Mathematical Sciences, Tel-Aviv University, Israel

Paul Biràn has made fundamental and influential contributions to symplectic topology as well as to algebraic geometry and Hamiltonian systems. His work is characterised by new depths in the interactions between complex algebraic geometry and symplectic topology. One of the earlier contributions is his surprising solution of the symplectic packing problem, completing work of Gromov, McDuff and Polterovich, showing that compact symplectic manifolds can be packed by symplectic images of equally sized Euclidean balls without wasting volume if the number of balls is not too small. Among the corollaries of his proof, Biràn obtains new estimates in the Nagata problem. A powerful tool in symplectic topology is Biràn's decomposition of symplectic manifolds into a disc bundle over a symplectic submanifold and a Lagrangian skeleton. Applications of this discovery range from the phenomenon of Lagrangian barriers to surprising novel results on topology of Lagrangian submanifolds. Paul Biràn not only proves deep results, he also discovers new phenomena and invents powerful techniques important for the future development of the field of symplectic geometry.

Elon Lindenstrauss, Clay Mathematics Institute, Massachusetts and Courant Institute of Mathematical Sciences, New York, USA

Elon Lindestrauss has done deep and highly original work at the interface of ergodic theory and number theory. Although he has worked widely in ergodic theory, his recent proof of the quantum unique ergodicity conjecture for arithmetic hyperbolic surfaces breaks fertile new ground, with great promise for future applications to number theory.

Already, in joint workwith Katok and Einsiedler, he has used some of the ideas in this work to prove the celebrated conjecture of Littlewood on simultaneous diophantine approximation for all pairs of real numbers lying outside a set of Hausdorff dimension zero. This goes far beyond what was known earlier about Littlewood's conjecture, and spectacularly confirms the high promise of themethods of ergodic theory in studying previously intractable problems of diophantine approximation.

Andrei Okounkov, Princeton University, USA

Andrei Okounkov contributed greatly to the field of asymptotic combinatorics. An extremely versatile mathematician, he found a wide array of applications of his methods. His early results include a proof of a conjecture of Olshanski on the representations theory of groups with infinite-dimensional duals. Okounkov gave the first proof of the celebrated Baik-Deift-Johansson conjecture, which states that the asymptotics of random partitions distributed according to the Plancherel measure coincides with that of the eigenvalues of large Hermitian matrices. An important and influential result of Okounkov is a formula he found in joint work with Borodin, which expresses a general Toeplitz determinant as the Fredholm determinant of the product of two associated Hankel operators. The new techniques of working with random partitions invented and successfully developed by Okounkov lead to a striking array of applications in a wide variety of fields: topology of module spaces, ergodic theory, the theory of random surfaces and algebraic geometry.

Sylvia Serfaty, Courant Institute of Mathematical Sciences, New York, USA

Sylvia Serfaty was the first to make a systematic and impressive asymptotic analysis for the case of large parameters in Theory of Ginzburg-Landau equation. She established precisely the values of the first, second and third (with E.Sandier) critical fields for nucleation of one stable vortex, vortex fluids and surface superconductivity. In micromagnetics, her work with F. Alouges and T. Rivière breaks new ground on singularly perturbed variational problems and provides the first explanation for the internal structure of cross-tie walls.

Stanislav Smirnov, KTH, Sweden and Geneva University, Switzerland

Stanislav Smirnov's most striking result is the proof of existence and conformal invariance of the scaling limit of crossing probabilities for critical percolation on the triangular lattice. This gives a formula for the limiting values of crossing probabilities, breakthrough in the field, which has allowed for the verification of many conjectures of physicists, concerning power laws and critical values of exponents. Stanislav Smirnov also made several essential contributions to complex dynamics, around the geometry of Julia sets and the thermodynamic formalism.

Xavier Tolsa, ICREA and Universitat Autònoma de Barcelona, Spain

Xavier Tolsa has made fundamental contributions to Harmonic and Complex Analysis. His most outstanding work solves Vitushkin's problem about semiadditivity of analytic capacity. The problem was raised in 1967 by Vitushkin in his famous paper on rational approximation in the plane. Tolsa's result has important consequences for a classical (100 years old) problem of Painlevé about a geometric characterization of planar compact sets are removable in the class of bounded analytic functions. Answering affirmatively Melnikov's conjecture, Tolsa provides a solution of the Painlevé problem in terms of the Menger curvature. Xavier Tolsa has also published many important and influential resultsrelated to Calderón-Zygmund theory and rational approximation in the plane.

Warwick Tucker, Uppsala University, Sweden

Warwick Tucker has given a rigorous proof that the Lorenz attractor exists for the parameter values provided by Lorenz. This was a long standing challenge to the dynamical system community, and was included by Smale in his list of problems for the new millennium. The proof uses computer estimates with rigorous bounds based on higher dimensional interval arithmetics. In later work, Warwick Tucker has made further significant contributions to the development and application of this area.

Otmar Venjakob, Mathematisches Institut Universität Heidelberg, Germany

Otmar Venjakob has made a number of important discoveries in both the algebraic and arithmetic aspects of non-commutative Iwasawa theory, especially on problems which appeared intractable from the point of view of the classical commutative theory. In arithmetic geometry, Iwasawa theory is the only general technique known for studying the mysterious relations between exact arithmetic formulae and special values of L-functions, as typified by the conjecture of Birch and Swinnerton-Dyer. Venjakob's work applies quite generally to towers of number fields whose Galois group is an arbitrary compact p-adic Lie group (which is not, in general, commutative), and has done much to show that a rich theory is waiting to be developed. His most important results include the proof of a good dimension theory for modules over Iwasawa algebras, and the proof of the first case of a structure theory for modules over these algebras. With Hachimori he discovered the first examples of arithmetic Iwasawa modules which are completely faithful, as well as proving a remarkable asymptotic upper bound for the rank of the Mordell Weil group of elliptic curves in certain towers of number fields over Q whose Galois group is a p-adic Lie group of dimension 2. Very recently, he found they key to the problem of defining, in non-commutative Iwasawa theory, the analogue of the characteristic series of modules over Iwasawa algebras.

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