Wolf Prize Laureate in Mathematics 2002/3
Affiliation at the time of the award:
Research Institute for Mathematical Sciences, Kyoto University, Japan
“for his creation of ‘algebraic analysis’, including hyperfunction and microfunction theory ,holonomic quantum field theory, and a unified theory of soliton equations.”
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.