Prof. George Lusztig (MIT)
Fourier transform as a triangular matrix
Tusday, June 15, 2026 - 16:30
Room 1C150 Torre Archimede
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Let V be a vector space of dimension 2n over the field F_2 with 2 elements. Assume that we are given a nondegenerate symplectic form on V with values in F_2. Let X be the vector space of complex valued functions on V. Fourier transform is an involution of X. We show that there exists an interesting basis of X in which the Fourier transform is upper triangular. This follows the tradition of Hermite who showed that the usual Fourier transform on the real line can be diagonalized.
Short Bio
George Lusztig (b. 1946, Timișoara) is Abdun Nur Professor of Mathematics at MIT. After studies in Bucharest and postdoctoral work with Michael Atiyah at the Institute for Advanced Study in Princeton, he joined MIT in 1978, where he has remained ever since.
Lusztig is one of the most influential mathematicians of our time, renowned for his groundbreaking contributions to representation theory. His work on algebraic groups, Hecke algebras, quantum groups, and finite groups of Lie type has shaped the field profoundly. Among his most celebrated achievements are the introduction of character sheaves, Deligne–Lusztig varieties, and Kazhdan–Lusztig polynomials.
His many honours include the Cole Prize (1985), the Brouwer Medal (1999), the Steele Prize for Lifetime Achievement (2008), the Shaw Prize (2014), the Wolf Prize in Mathematics (2022), and the Basic Science Lifetime Award (2025). He was three times speaker at the ICM: plenary in 1990, while in 1983 in the section `Lie groups & representations' and in 1974 in the section `Algebraic Groups & Discrete Subgroups'.
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