15:00-16:00
Masao Oi (NTU)

Title: Local Langlands conjecture and positive-depth Deligne-Lusztig theory

Abstract: The local Langlands conjecture predicts that irreducible representations of a p-adic reductive group can be classified in terms of certain arithmetic data involving local Galois representations. One possible approach to the local Langlands conjecture is to find some nice parametrization of irreducible representations of a p-adic reductive group because it typically enables us to construct the corresponding local Galois representations in an explicit manner.
On the other hand, by Deligne-Lusztig theory, it is known that any irreducible representation of a finite reductive group can be realized on the etale cohomology of an algebraic variety called the Deligne–Lusztig variety. Recently, Chan–Ivanov established a generalization of Deligne–Lusztig theory, which provides representations of open compact subgroups of a p-adic reductive group.
In this talk, I would like to discuss the relationship between Chan–Ivanov’s representations and a certain class of representations of a p-adic reductive group, especially, from the viewpoint of the local Langlands conjecture.
This talk is based on my joint work with Charlotte Chan (University of Michigan).

16:30-17:30
Wee Teck Gan (NUS)

Title: Global Langlands parameters for G_2

Abstract: I will discuss a joint work with Erez Lapid which gives a characterization of those automorphic representations of GL(7) which arise as the functorial lifts from globally generic cuspidal representations of the exceptional group G_2. This refines earlier results of Joseph Hundley and Baiying Liu and gives rise to a notion of global L-parameters for G_2.