# Ilya Piatetski-Shapiro

Wolf Prize Laureate in Mathematics 1990

**Ilya Piatetski-Shapiro**

#### Affiliation at the time of the award:

**Tel Aviv University, ****Israel**

#### Award citation:

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

#### Prize share:

**Ilya Piatetski-Shapiro**

**Ennio De Giorgi **

Ilya Piatetski-Shapiro (born in 1929, Russia) developed a fascination for mathematics at the age of 10. His curiosity was ignited by the unique beauty of negative numbers, a subject introduced to him by his father, a Ph.D. in chemical engineering. While still an undergraduate at Moscow University, Piatetski-Shapiro’s mathematical prowess earned him the Moscow Mathematical Society Prize for a Young Mathematician in 1952. The winning paper he presented contained a solution to the problem posed by the French analyst Raphaël Salem regarding sets of uniqueness of trigonometric series.

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).