Local Langlands correspondence and affine Hecke algebras

：Anne-Marie Aubert（Institut de Mathématiques de Jussieu – Paris Rive Gauche,C.N.R.S., Sorbonne Université, Université Paris Cité）
：2023-11-05 09:00
：厦门大学海韵园实验楼105报告厅

报告人：Anne-Marie Aubert（Institut de Mathématiques de Jussieu – Paris Rive Gauche,C.N.R.S., Sorbonne Université, Université Paris Cité）

时  间：2023年11月5日09:00

地  点：厦门大学海韵园实验楼105报告厅

内容摘要:

The irreducible smooth representations of p-adic reductive groups and the enhanced Langlands parameters of these latter can both be partitioned into series indexed by certain cuspidal data. On the representation side, cuspidality refers to supercuspidal representations of Levi subgroups, while on the Galois side it refers to cuspidal unipotent pairs, as introduced by Lusztig, in certain subgroups of the Langlands dual groups. In addition, on both sides of the correspondence, the elements in a given series are in bijection with the simple modules of a generalized affine Hecke algebra. We will review these results and explain how they can be used in order to build the local Langlands correspondence.

个人简介：

Anne-Marie Aubert is a prominent French mathematician who specializes in the Langlands program, Representation Theory, and Noncommutative Geometry. She defended her Ph.D Thesis at Université Paris VII in 1990 under the supervision of Jean-Loup Waldspurger, and her Habilitation from Université Paris Sud in 1997. She is currently Director of Research of Exceptional Class at the Centre National de la Recherche Scientifique (C.N.R.S.) and the Chief of the Automorphic Forms team at the Institut Mathématiques de Jussieu - Paris Rive Gauche. She is a member of the Council of IMJ-PRG and the UFR of Mathematics of the Université Paris Cité. She has been member of the Office of the CoCNRS (Section 41: Mathematics and interactions of mathematics) from 2015-2021, and member of the Comité 40 of the French National Research Agency (A.N.R.) from 2019-2022. In 2019-2021, she was the chair of the Committee To Select the Winner of the Chevalley Prize in Lie Theory of the American Mathematical Society and co-leader of the MATH-AmSud project Number Theory: interconnections with Algebra, Combinatorics and Representation Theory. Since 2019, she has been the Managing Editor of Representation Theory, an electronic journal of the Amer. Math. Soc.

联系人：余世霖