Ilya Piatetski-Shapiro

Ilya Piatetski-Shapiro Winner of Wolf Prize in Mathematics - 1990
Ilya Piatetski-Shapiro


The Mathematics Prize committee has unanimously selected the following two candidates to equally share the 1990 Wolf Prize in Mathematics:

Ilya Piatetski-Shapiro
Tel Aviv University
Tel Aviv, Israel

for his fundamental contributions in the fields of homogeneous complex domains, discrete groups, representation theory and automorphic forms

Ennio De Giorgi
Scuola Normale Superiore
Pisa, Italy

for his innovating ideas and fundamental achievements s in partial differential equations and calculus of variations.

The work of Professor Ennio De Giorgi is among the most important and creative accomplishments in the theory of partial differential equations and the calculus of variations. At the time he began his studies, mathematicians were not able to handle anything beyond second order nonlinear elliptic equations in two variables. In his first major break-through in 1957, De Giorgi proved that solutions of uniformly elliptic second order equations of divergence form with only measurable coefficients were Holder continuous.
Probably his greatest contribution cue in 1960; this was a regularity theory for minimal hypersurfaces. Such surfaces arise as surfaces of smallest area spanning a given boundary. The proof required De Giorgi to develop his own version of what we now call geometric measure theory along with a related key compactness theorem. He was then able to conclude that a minimal hypersurface is analytic outside a closed subset of codimension at least two. Since then he and his school have settled litany of the outstanding problems in this area.

For almost 40 years Professor Ilya Piatetski-Shapiro has been making major contributions in mathematics by solving outstanding open problems and by introducing new ideas in the theory of automorphic functions and its connections with number theory, algebraic geometry and infinite dimensional representations of Lie groups. His work has been a major, often decisive factor in the enormous progress in this theory during the last three decades.
Among his main achievements are: the solution of Salem´s problem about the uniqueness of the expansion of a function into a trigonometric series; the example of a non symmetric homogeneous domain in dimension 4 answering Cartan´s question, and the complete classification (with E. Vinberg and G. Gindikin) of all bounded homogeneous domains; the solution of Torelli´s problem for K-3 surfaces (with I. Shafarevich); a solution of a special case of Selberg´s conjecture on unipotent elements, which paved the way for important advances in the theory of discrete groups, and many important results in the theory of automorphic functions, e.g., the extension of the theory to the general context of semi-simple Lie groups (with I. Gelfand), the general theory of arithmetic groups operating on bounded symmetric domains, the first 'converse theorem” for GL(3), the construction of L-functions for automorphic representations for all the classical groups (with S. Rallis) and the proof of the existence of non arithmetic lattices in hyperbolic spaces of arbitrary large dimension (with M. Gromov).