Vortrag am Montag, 08.07.2024, 14:15 Uhr, in IA 1/75

Vortragender: Alexander Ivanov (RUB)

Titel: "An introduction to the Langlands correspondences"

Abstract:
I will try to explain some basics of the Langlands program, with as few prerequisites as possible. More concretely, I will concentrate on the case of number fields (the original case, where Langlands program took its origin) and discuss in detail the one-dimensional case --that is, global class field theory. Then I will sketch the n-dimensional conjecture.

Vortrag am Montag, 03.06.2024, 14:15 Uhr, in IA 1/75

Vortragender: Jakub Löwit (IST)

Titel: "On modular p-adic Deligne--Lusztig theory for GL_n"

Abstract:
In 1976, Deligne--Lusztig realized the characteristic zero representation theory of finite groups of Lie type inside cohomology of certain algebraic varieties. This picture has two interesting generalizations. In one direction, one can replace finite groups by p-adic groups. In another direction, one can consider modular coefficients. After recalling the key players, I will discuss what happens in the p-adic case with modular coefficients for GL_n. In particular, I will explain how to deduce such results from the case of characteristic zero coefficients.

Vortrag am Montag, 15.04.2024, 14:15 Uhr, in IA 1/75

Vortragender: David Schwein (University of Bonn)

Titel: "Tame supercuspidals at very small primes"

Abstract:
Supercuspidal representations are the elementary particles in the representation theory of reductive p-adic groups. Constructing such representations explicitly, via (compact) induction, is a longstanding open problem, solved when p is large. When p is small, the remaining supercuspidals are expected to have an arithmetic source: wildly ramified field extensions. In this talk I'll discuss ongoing work joint with Jessica Fintzen that identifies a second, Lie-theoretic, source of new (tame!) supercuspidals: special features of reductive groups at very small primes. We'll summarize some of these features and explain how they contribute to the construction of supercuspidals.