George Lusztig | |
|---|---|
| Born | May 20, 1946 |
| Citizenship | Romanian, British, American |
| Alma mater | University of Bucharest (BSc) Princeton University (PhD) |
| Known for | Crystal base Deligne–Lusztig theory Kazhdan–Lusztig polynomial |
| Awards | ICM Speaker (1974, 1983, 1990) Berwick Prize (1977) Guggenheim Fellowship (1982) FRS (1983) Cole Prize (1985) Brouwer Medal (1999) Leroy P. Steele Prize (2008) Shaw Prize (2014) Wolf Prize in Mathematics (2022) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Warwick Massachusetts Institute of Technology |
| Doctoral advisor | Michael Atiyah William Browder |
| Doctoral students | Corrado de Concini Ian Grojnowski Xuhua He |
George Lusztig (born Gheorghe Lusztig; May 20, 1946) is a Romanian-born American mathematician and Abdun Nur Professor at the Massachusetts Institute of Technology (MIT). He was a Norbert Wiener Professor in the Department of Mathematics from 1999 to 2009.
Born in Timișoara to a Hungarian-Jewish family, [1] he did his undergraduate studies at the University of Bucharest, graduating in 1968. Later that year he left Romania for the United Kingdom, where he spent several months at the University of Warwick and Oxford University. In 1969 he moved to the United States, where he went to work for two years with Michael Atiyah at the Institute for Advanced Study in Princeton, New Jersey. He received his PhD in mathematics in 1971 after completing a doctoral dissertation, titled "Novikov's higher signature and families of elliptic operators", under the supervision of William Browder and Michael Atiyah. [2] [3]
Lusztig worked for almost seven years at the University of Warwick. His involvement at the university encompassed a Research Fellowship, (1971–72); lecturer in Mathematics, (1972–74); and Professor of Mathematics, (1974–78). In 1978, he accepted a chair at MIT. [4] [1]
He is known for his work on representation theory, in particular for the objects closely related to algebraic groups, such as finite reductive groups, Hecke algebras, -adic groups, quantum groups, and Weyl groups. He essentially paved the way for modern representation theory. This has included fundamental new concepts, including the character sheaves, the Deligne–Lusztig varieties, and the Kazhdan–Lusztig polynomials. [5]
In 1983, Lusztig was elected as a fellow of the Royal Society. [4] In 1985 Lusztig won the Cole Prize (Algebra). He was elected to the National Academy of Sciences in 1992. He received the Brouwer Medal in 1999, the National Order of Faithful Service in 2003 and the Leroy P. Steele Prize for Lifetime Achievement in Mathematics in 2008. In 2012, he became a fellow of the American Mathematical Society [6] and in 2014 he received the Shaw Prize in Mathematics. [7] In 2022, he received the Wolf Prize in Mathematics. [8]
Sir Michael Francis Atiyah was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004.
Isadore Manuel Singer was an American mathematician. He was an Emeritus Institute Professor in the Department of Mathematics at the Massachusetts Institute of Technology and a Professor Emeritus of Mathematics at the University of California, Berkeley.
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index is equal to the topological index. It includes many other theorems, such as the Chern–Gauss–Bonnet theorem and Riemann–Roch theorem, as special cases, and has applications to theoretical physics.
David Bryant Mumford is an American mathematician known for his work in algebraic geometry and then for research into vision and pattern theory. He won the Fields Medal and was a MacArthur Fellow. In 2010 he was awarded the National Medal of Science. He is currently a University Professor Emeritus in the Division of Applied Mathematics at Brown University.
Sergei Petrovich Novikov was a Soviet and Russian mathematician, noted for work in both algebraic topology and soliton theory. He became the first Soviet mathematician to receive the Fields Medal in 1970.
Sir Simon Kirwan Donaldson is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. He is currently a permanent member of the Simons Center for Geometry and Physics at Stony Brook University in New York, and a Professor in Pure Mathematics at Imperial College London.
Nigel James Hitchin FRS is a British mathematician working in the fields of differential geometry, gauge theory, algebraic geometry, and mathematical physics. He is a Professor Emeritus of Mathematics at the University of Oxford.
Vladimir Gershonovich Drinfeld, surname also romanized as Drinfel'd, is a mathematician from the former USSR, who emigrated to the United States and is currently working at the University of Chicago.
Michael Artin is an American mathematician and a professor emeritus in the Massachusetts Institute of Technology Mathematics Department, known for his contributions to algebraic geometry.
Dusa McDuff FRS CorrFRSE is an English mathematician who works on symplectic geometry. She was the first recipient of the Ruth Lyttle Satter Prize in Mathematics, was a Noether Lecturer, and is a Fellow of the Royal Society. She is currently the Helen Lyttle Kimmel '42 Professor of Mathematics at Barnard College.
Victor Matveevich Buchstaber is a Soviet and Russian mathematician known for his work on algebraic topology, homotopy theory, and mathematical physics.
Dennis Parnell Sullivan is an American mathematician known for his work in algebraic topology, geometric topology, and dynamical systems. He holds the Albert Einstein Chair at the Graduate Center of the City University of New York and is a distinguished professor at Stony Brook University.
Alexander A. Beilinson is the David and Mary Winton Green University professor at the University of Chicago and works on mathematics. His research has spanned representation theory, algebraic geometry and mathematical physics. In 1999, Beilinson was awarded the Ostrowski Prize with Helmut Hofer. In 2017, he was elected to the National Academy of Sciences. In 2018, he received the Wolf Prize in Mathematics and in 2020 the Shaw Prize in Mathematics.
Wolfgang Lück is a German mathematician who is an internationally recognized expert in algebraic topology.
Minhyong Kim (Korean: 김민형) is a South Korean mathematician who specialises in arithmetic geometry and anabelian geometry.
John Roe was a British mathematician.
Guoliang Yu is a Chinese American mathematician. After receiving his Ph.D from SUNY at Stony Brook in 1991 under the direction of Ronald G. Douglas, Yu spent time at the Mathematical Sciences Research Institute (1991–1992), the University of Colorado at Boulder (1992–2000), Vanderbilt University (2000–2012), and a variety of visiting positions. He currently holds the Powell Chair in Mathematics and was appointed University Distinguished Professor in 2018 at Texas A&M University. He is a fellow of the American Mathematical Society.
Geordie Williamson is an Australian mathematician at the University of Sydney. He became the youngest living Fellow of the Royal Society when he was elected in 2018 at the age of 36.
Henri Moscovici is a Romanian-American mathematician, specializing in non-commutative geometry and global analysis.
Xuhua He is a Chinese mathematician and Chair Professor at the University of Hong Kong.
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