George Lusztig, the Abdun-Nur Professor of Mathematics, was awarded the Shaw Prize in Mathematical Sciences for 2014. The Shaw Foundation cited Lusztig “for his fundamental contributions to algebra, algebraic geometry, and representation theory, and for weaving these subjects together to solve old problems and reveal beautiful new connections.”
The $1 million annual prize is awarded in three categories — astronomy, life science and medicine, and mathematical sciences — to individuals who have made outstanding contributions in academic and scientific research or applications.
After Lusztig graduated from the University of Bucharest in 1968, he received an master's and PhD from Princeton University in 1971 under the direction of Michael Atiyah and William Browder. He joined MIT's Department of Mathematics in 1978 following a professorship at the University of Warwick.
Through the 1970s and 1980s, Lusztig, in part with Pierre Deligne, gave a complete description of representations of finite Chevalley groups, the building blocks of finite symmetry groups. The Deligne–Lusztig description, introduced in 1976, uses the topology and geometry of Schubert varieties (a tool used to count solutions of algebraic equations). Correspondences identified in the Deligne-Lusztig description between the algebraic subtleties of representation theory and the geometric/topological subtleties of Schubert varieties would form a major theme in Lusztig’s work.
Lusztig would go on to show that many central problems in representation theory, such as those of real and p-adic groups, can be related to topology and geometry by means of Schubert varieties. This work would form the basis for many important recent developments, such as progress in the Langlands program and automorphic forms.
Beginning with a 1979 paper with David Kazhdan, and continuing through his most recent work, Lusztig has found combinatorial tools to describe the topology and geometry of Schubert varieties and the representations to which they are related. While these tools are easy to describe, they had not been used previously in mathematics.
“George Lusztig has unveiled profound connections between areas of mathematics that had previously been thought of as having no common overlap,” says Michael Sipser, interim dean of the School of Science. “In the course of doing so he shaped much of modern mathematics.”
In addition to the Shaw Prize, Lusztig has been distinguished with numerous honors. Among them are: the Berwick Prize of the London Mathematical Society; the AMS Cole Prize in Algebra; the Brouwer Medal of the Dutch Mathematical Society; and the AMS Leroy P. Steele Prize for Lifetime Achievement. Lusztig is a fellow of the Royal Society, a fellow of the American Academy of Arts and Sciences, and a member of the National Academy of Sciences.