Ilya Piatetski-Shapiro

Ilya Josifowitsch Pjatetskij - Shapiro (Hebrew איליה פיאטצקי - שפירו; Russian Илья Иосифович Пятецкий - Шапиро; born March 30, 1929 in Moscow, † February 21, 2009 in Tel Aviv ) was a Russian -born Israeli mathematician, who is with representation theory discrete groups, homogeneous complex spaces and automorphic functions employed.

Pjatetskij - Shapiro visited in 1946 the Moscow State University and heard among others, Alexander Gelfond and Nina Bari. After completing a PhD position him from the party was denied ( he came from a Jewish family, his father was an engineer ). But Gelfond gave him a job at the Pedagogical Institute, where he received his doctorate at Alexander Book rod 1954. Then he was sent as a teacher to Kaluga. In 1958, he managed to get a job at the Keldysh Institute of Applied Mathematics in Moscow. He dealt with the theory of automorphic functions and participated in the seminar on this topic by Igor Shafarevich. Pjatetskij - Shapiro was a professor at Moscow University, where he was a close colleague of Israel Gelfand, and later at Yale University and at the University of Tel Aviv.

His main field of work is the theory of automorphic functions and its application in geometry and number theory. With Israel Gelfand, he expanded the theory of automorphic functions on semisimple Lie groups. He solved the problem of Salem on the uniqueness of the development of a function in a trigonometric series. With Shafarewitsch he solved Torelli problem for K -3 surfaces. With Gindikin and Vinberg he classified all finite homogeneous areas. He found an example of a non- symmetric homogeneous field in the Dimension 4 ( which he solved a problem of Elie Cartan ). He developed the general theory of arithmetic groups on limited symmetric spaces. With Rallis he constructed the functions for all automorphic representations of classical groups. With Gromov he proved the existence of arithmetic lattice in hyperbolic spaces of arbitrarily high dimension.

In 1981 he was awarded the Israel Prize, the Wolf Prize in 1990. In 1966 he gave a plenary lecture at the International Congress of Mathematicians in Moscow ( automorphic functions and Arithmetic groups), and in 1978 he was invited speaker at the ICM in Helsinki ( Tate theory for reductive groups and distinguished representations ). In 2002 he was invited speaker at the International Congress of Mathematicians in Beijing ( Converse theorems, functoriality and applications to number theory, with JW Cogdell ).

Writings

  • With J. Cogdell: The Arithmetic and Spectral Analysis of Poincaré Series. Perspectives in Mathematics Vol 13, Academic Press, 1990.
  • With D.Ginzburg, Rallis: - Functions for the orthogonal group. Memoirs AMS 1997.
  • James Cogdell, Simon Gindikin, Peter Sarnak (Editor ): Selected Works of Ilya Piatetski - Shapiro. American Mathematical Society, 2000.
  • Complex representations of finite fields for. American Mathematical Society in 1983.
  • With Israel Gelfand, Graev: Representation Theory and automorphic functions. Generalized Functions Bd.6, Academic Press 1990.
  • With Stephen Gelbart, Rallis: Explicit construction of automorphic - functions. Springer -Verlag 1987.
  • Automorphic functions and the geometry of classical domains. Gordon and Breach 1969.
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