THE 2002/3 WOLF FOUNDATION PRIZE IN MATHEMATICS

The Prize Committee for Mathematics has unanimously decided that the 2002/3 Wolf Prize be jointly awarded to:**Mikio SatoResearch Institute for Mathematical SciencesKyoto UniversityKyoto, Japan**

for his creation of “algebraic analysis´, including hyperfunction and microfunction theory,holonomic quantum field theory, and a unified theory of soliton equations.

John T. Tate

Department of Mathematics

University of Texas

Austin, Texas, USA

for his creation of fundamental concepts in algebraic number theory.

Professor Mikio Sato´s vision of “algebraic analysis' and mathematical physics initiated several fundamental branches of mathematics. Sato created the theory of hyperfunctions and invented microlocal analysis, that allowed for a description of the structure of singularities of (hyper)functions on cotangent bundles. Hyperfunctions, together with integral Fourier operators, have become a major tool in linear partial differential equations. Along with his students, Sato developed holonomic quantum field theory, providing a far-reaching extension of the mathematical formalism underlying the two-dimensional Ising model and introduced along the way the famous tau functions. Sato provided a unified geometric description of soliton equations in the context of tau functions and infinite dimensional Grassmann manifolds. This was extended by his followers to other classes of equations, including self dual Yang-Mills and Einstein equations. Sato has generously shared his ideas with young mathematicians and has created a flourishing school of algebraic analysis in Japan.

For over a quarter of a century, Professor John Tate´s ideas have dominated the development of arithmetic algebraic geometry. Tate has introduced path breaking techniques and concepts, that initiated many theories which are very much alive today. These include Fourier analysis on local fields and adele rings, Galois cohomology, the theory of rigid analytic varieties, and p-divisible groups and p-adic Hodge decompositions, to name but a few. Tate has been an inspiration to all those working on number theory. Numerous notions bear his name: Tate cohomology of a finite group, Tate module of an abelian variety, Tate-Shafarevitch group, Lubin-Tate groups, Neron-Tate heights, Tate motives, the Sato-Tate conjecture, Tate twist, Tate elliptic curve, and others. John Tate is a revered name in algebraic number theory.