May 15, 2025
Interaction of the local Langlands program with the generalized Springer correspondence
Algebraic Geometry and Number Theory Seminar
Date: May 15, 2025 |
1:00 pm –
3:00 pm
Speaker:
Anna-Marie Aubert, IMJ-PRG
Location: Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101)
Language:
English
(I) Born in a letter of Robert Langlands to Andr Weil in 1967, the Langlands program seeks to establish a far-reaching tissue of conjectures relating seemingly distant areas of mathematics, primarily number theory, representation theory, and algebraic geometry.
I will give a survey of the local Langlands correspondence, which is at the core of the program, on both real and p-adic groups, and will illustrate it on several examples.
(II) The Springer correspondence is an injective map from the set of irreducible representations of the Weyl group W of a complex connected reductive group G to the set of simple G-equivariant perverse sheaves on the nilpotent cone. In 1984, Lusztig promoted it to a bijective map by replacing the group W by a collection of relative Weyl groups. I will first explain Lusztig's construction and its extension to possibly disconnected reductive groups. Next, I will describe the role it plays in the Langlands correspondence for p-adic groups thanks to a Galois analogue of the Bernstein Center.
