George Lusztig

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George Lusztig , actually Gheorghe Lusztig , (* 1946 in Timișoara , Romania ) is an American mathematician who deals with representation theory.

Lusztig studied at the University of Bucharest . He then went to the USA, where he worked with Michael Atiyah at the Institute for Advanced Study in Princeton from 1969 to 1971 . In 1971 he received his doctorate in Princeton with Atiyah and (formally) William Browder ( Novikov's Higher Signature and Families of Elliptic Operators , published in Journal of Differential Geometry Vol. 7, 1972, p. 229). From 1971 he was at the University of Warwick in England, where he was lecturer in 1972 and professor in 1974. From 1978 he was at the Massachusetts Institute of Technology (MIT), where he is currently Norbert Wiener Professor .

His dissertation was an essential contribution to the Novikov conjecture .

Lusztig introduced new fundamental concepts to the representation theory of algebraic groups . In the Deligne-Lusztig theory (with Pierre Deligne , Representations of reductive groups over finite fields , Annals of Mathematics, Vol. 103, 1976, pp. 103–161) the -adic cohomology is used to create linear representations of finite groups from Lie- Construct type . In 1984 Lusztig gave all representations of finite simple groups of the Lie type. In the paper Representation of Coxeter groups and Hecke algebras ( Inventiones Mathematicae Vol. 53, 1979, p. 165) Kazhdan and Lusztig introduced Kazhdan-Lusztig polynomials in 1979 (and formulated the Kazhdan-Lusztig conjectures ) and provided an interpretation in 1980 the cut cohomology of Goresky and Robert MacPherson . Lusztig lectured on the application of these "geometric" methods in representation theory at the International Congress of Mathematicians in Kyoto in 1990 ( Intersection Cohomology Methods in Representation Theory ). From the late 1980s he also dealt with quantum groups (defined in 1985 by Wladimir Drinfeld and Michio Jimbō ).

In 1977 he received the Junior Berwick Prize of the London Mathematical Society and in 1985 the Cole Prize in Algebra. He has been an elected member of the American Academy of Arts and Sciences since 1991, the National Academy of Sciences since 1992 , and he is a fellow of the American Mathematical Society . In 1999 he received the Brouwer Medal and in 2008 the Leroy P. Steele Prize . In 1974 he was invited speaker at the International Congress of Mathematicians in Vancouver ( On the discrete series representations of the classical groups over finite fields ) as well as in 1983 in Warsaw ( Characters of reductive groups over finite fields ) and in 1990 in Kyoto ( Intersection cohomology methods in representation theory ). In 2014 he was awarded the $ 1 million Shaw Prize in Mathematics.

His PhD students included Ian Grojnowski (1992) and Corrado de Concini .

Fonts

  • Publications of George Lusztig. In: Nagoya Mathematical Journal. Volume 182 (Special Issue Celebrating the 60th Birthday of George Lusztig), 2006, pp. I-XI, ( online ).
  • The Discrete Series of GL n over a Finite Field (= Annals of Mathematical Studies. 81). Princeton University Press et al., Princeton NJ 1974.
  • with Pierre Deligne : Representations of reductive groups over finite fields. In: Annals of Mathematics . Series 2, Vol. 103, No. 1, 1976, pp. 103-161, doi : 10.2307 / 1971021 .
  • with David Kazhdan : Representations of Coxeter Groups and Hecke Algebras. In: Inventiones Mathematicae . Volume 53, No. 2, 1979, pp. 165-184 .
  • with David Kazhdan: Schubert varieties and Poincaré duality. In: Robert Osserman , Alan Weinstein (Eds.): Geometry of the Laplace Operator. (Proceedings of the Symposium in Pure Mathematics of the American Mathematical Society. Held at the University of Hawaii, Honolulu, Hawaii, March 27-30, 1979) (= Proceedings of Symposia in Pure Mathematics. 36). American Mathematical Society, Providence RI 1980, ISBN 0-8218-1439-7 , pp. 185-203.
  • Characters of Reductive Groups over a Finite Field (= Annals of Mathematical Studies. 107). Princeton University Press, Princeton NJ 1984, ISBN 0-691-08351-7 .
  • Introduction to Quantum Groups (= Progress in Mathematics. 110). Birkhäuser, Boston MA et al. 1993, ISBN 0-8176-3712-5 .

literature

Web links

Individual evidence

  1. ↑ Steven C. Ferry, Andrew Ranicki , Jonathan Rosenberg : A history and survey of the Novikov conjecture. In: Steven C. Ferry, Andrew Ranicki, Jonathan M. Rosenberg (Eds.): Novikov Conjectures, Index Theorems and Rigidity. Oberwolfach 1993 (= London Mathematical Society. Lecture Note Series. 226). Cambridge University Press, Cambridge 1995, ISBN 0-521-49796-5 , pp. 7-66, ( digitized ).
  2. ^ Proved in 1981 by Jean-Luc Brylinski and Masaki Kashiwara and independently by Alexander Beilinson and Joseph Bernstein .
personal data
SURNAME Lusztig, George
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH 1946
PLACE OF BIRTH Timișoara , Romania