On the compactification of mini-Vogan varieties V and the restriction functor D_P(G/P) --> D_H(V).

Clifton and Qing in Calgary, Geo in Radboud and Andrew in Lethbridge

Location: Zoom

Speakers: James Steele and André de Waal

We continue our study of the quiver category A_n and the four functors

J^* : A_n --> A_0,
J_* : A_0 --> A_n,
J_! : A_0 --> A_n and
J_{!*} : A_0 --> A_n.

The goal of the talk is to prove Propositions 3.3, 3.5 and 3.6 of Section 3.2 of Tom Braden's thesis.

Speaker: Qing Zhang

Qing and Clifton have now computed all ABV-packets for all unipotent Arthur parameters of the exceptional group G(2). The results are summarized in this talk.

Speaker: Geoff Vooys

In this talk we will introduce the Bernstein Decomposition and describe the Bernstein Centre of the category of smooth representations of the F-rational points of a p-adic group G. We will then describe how to realize the Bernstein Centre as a ring of sections of a variety, and, time permitting, use this to explain the parametrization of the Bernstein Decomposition.

Nicole will update us on her progress toward calculating the microlocal vanishing cycles of the Kashiwara-Saito singularity.

Clifton will make a small correction to the geometric multiplicity matrix for the admissible representations of G(2) with “subregular unipotent” infinitesimal parameter.
Qing will explain that he’s found all the admissible representations and standard modules of G(2) with “subregular unipotent” infinitesimal parameter and that the multiplicity matrix matches the geometric calculation. This concludes the proof of the Kazhdan-Lusztig conjecture (as it appears in the Voganish book) for the subregular unipotent infinitesimal parameter of G(2).

Presentation at the MATRIX conference on Geometric and Categorical Representation Theory

Title: Toward a geometrisation of functions on the integral points of p-adic varieties

Abstract: In this talk we will see how to define a topology on the category of formal schemes over the p-adic integers whose fundamental group coincides with the {\'e}tale fundamental group of Fp-schemes.

Speaker: Geoff Vooys

Presentation at the MATRIX conference on Geometric and Categorical Representation Theory

Title: The geometry of local Arthur packets

Speaker: Clifton Cunningham

Abstract: This talk explains how an Arthur parameter determines a category of perverse sheaves and how the microlocal perspective on this category reveals an Arthur packet.