David Kazhdan

David Kazhdan (Russian: Дмитрий Александрович Каждан, Dmitry Alexandrovich Kaschdan; Hebrew דוד קשדן; * 1946 in Moscow ) is a formerly working in the Soviet Union, Israeli mathematician who deals with representation theory.

Life and work

David Kazhdan is the son of the famous Byzantinists Alexander Kazhdan and received his doctorate in 1969 in Moscow with Alexander Kirillov. After that, he was a member of the school of Israel Gelfand in Moscow before emigrating as a Jew in 1975 in the USA, where he changed his name. He went to Harvard University, where he became a professor. 2005 emigrated to Israel and is currently a professor at the Hebrew University and at Harvard.

Kazhdan worked in the representation theory of Lie groups, Lie algebras and algebraic groups. There, the Kazhdan - Lusztig conjectures are named on identities between characters of Verma modules ( special representations of Lie algebras ) after him and George Lusztig, which have been proved independently by Alexander Beilinson and Joseph Bernstein and Masaki Kashiwara and Jean -Luc Brylinski 1981. In the assumptions and the Lusztig polynomials defined by it be used. They are defined with the help of the Weyl groups of the Lie algebras and were originally studied by Lusztig and Kazhdan in connection with the geometry of Schubert varieties, which are often studied as examples of singular algebraic varieties. The Kazhdan - Lusztig polynomials provide a kind of measure of the singularity of these varieties and were brought by Kazhdan and Lusztig with the cut - cohomology by Goresky MacPherson and in combination. An important concept in group theory is Kazhdans property T.

Since 2006 he is member of the Israel Academy of Sciences. His doctoral include Vladimir Voevodsky and Alexander Polishchuk. In 1990 he was MacArthur Fellow. In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley ( Algebraic Geometry and Representation Theory). In 2012 he gave a plenary lecture at the European Congress of Mathematicians (ECM ) in Krakow ( Representations of affine Kac - Moody groups over local and global fields ).

He has three sons and a daughter. His son Eli is a politician in Israel, his son Michael a professor of computer science at Johns Hopkins University.