Ilya Pyatetsky-Shapiro

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

Pyatetsky-Shapiro in Yale 1985

Pyatetskij-Shapiro attended Lomonosov University from 1946 and heard from Alexander Gelfond and Nina Bari , among others . After graduating, the party refused him a doctoral position (he came from a Jewish family, his father was an engineer). But Gelfond got him a position at the Pedagogical Institute, where he received his doctorate in 1954 under Alexander Buchab. Then he was sent to Kaluga as a school teacher . In 1958 he managed to get a job at the Keldysh Institute for Applied Mathematics in Moscow. He dealt with the theory of automorphic functions and took part in Igor Schafarewitsch's seminar on this topic. Pyatetsky-Shapiro was a professor at Moscow University, where he was a close collaborator with Israel Gelfand , and later at Yale University and Tel Aviv University .

His main field of work was the theory of automorphic functions and their application in geometry and number theory. With Israel Gelfand, he extended the theory of automorphic functions to semi-simple Lie groups. He solved Salem's problem about the uniqueness of the expansion of a function in a trigonometric series. With Schafarewitsch he solved Torelli's problem for K-3 surfaces. With Gindikin and Vinberg he classified all limited homogeneous areas. He found an example of a nonsymmetrical homogeneous area in dimension 4 (thus solving an Élie Cartan's problem). He developed the general theory of arithmetic groups on limited symmetrical spaces. With Rallis he constructed the functions for all automorphic representations of classical groups. With Gromow he proved the existence of arithmetic lattices in hyperbolic spaces of arbitrarily high dimensions. ${\displaystyle L}$

In 1981 he received the Israel Prize , in 1990 the Wolf Prize . 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 James Cogdell ).

Fonts

• with J. Cogdell: The Arithmetic and Spectral Analysis of Poincaré Series. Perspectives in Mathematics Vol. 13, Academic Press, 1990.
• with D. Ginzburg, Stephen Rallis : -Functions for the orthogonal group. Memoirs AMS 1997. ${\displaystyle L}$
• James Cogdell, Simon Gindikin , Peter Sarnak (Editors): Selected Works of Ilya Piatetski-Shapiro. American Mathematical Society, 2000.
• Complex representations of finite fields ${\displaystyle GL(2,K)}$ ${\displaystyle K}$ . American Mathematical Society 1983.
• with Israel Gelfand , Graev : Representation Theory and automorphic functions. Generalized Functions Vol. 6, Academic Press 1990.
• with Stephen Gelbart , Rallis: Explicit construction of automorphic -Functions. ${\displaystyle L}$Springer-Verlag 1987.
• Automorphic functions and the geometry of classical domains. Gordon and Breach 1969.

literature

• Stephen Gelbart (editor): Festschrift in Honor of IIPiateski-Shapiro on Occasion of his 60th Birthday. 2 vols., Weizmann Institute of Science Press 1990.
• Vladimir Tikhomirow: Moscow Mathematics 1950–1975. In: Jean-Paul Pier: Development of Mathematics 1950-2000. 2000.

Web links

• Ilja Pjatetskij-Shapiro in the Mathematics Genealogy Project (English)
• Wolf Prize for Pyatetsky Shapiro