James Mracek thesis defence, Part 1

Title: Applications of algebraic microlocal analysis in symplectic geometry and representation theory
Location: BA6183, Bahen Center, 40 St. George St.
Speaker: James Mracek
Speaker URL:
Institution: University of Toronto

PhD Advisors: Lisa Jeffrey – Clifton Cunningham


This thesis investigates applications of microlocal geometry in both representation theory and symplectic geometry. Accordingly, there are two bodies of work contained herein.

The first part of this thesis investigates a conjectural geometrization of local Arthur packets. These packets of representations of a p-adic group were invented by Arthur for the purpose of classifying the automorphic discrete spectrum of special orthogonal and symplectic groups. While their existence has been established, an explicit construction of Arthur packets remains difficult. In the case of real groups, Adams, Barbasch, and Vogan showed how one can use a geometrization of the local Langlands correspondence to construct packets of equivariant D-modules that satisfy similar endoscopic transfer properties as the ones defining Arthur packets. We classify the contents of these “microlocal” packets in the analogue of these varieties for p-adic groups, under certain restrictions, for a plethora of split classical groups.

The goal of the second part of this thesis is to find a way to make sense of the Duistermaat-Heckman function for a Hamiltonian action of a compact torus on an infinite dimensional symplectic manifold. We show that the Duistermaat-Heckman theorem can be understood in the language of hyperfunction theory, then apply this generalization to study the Hamiltonian T×S1 action on ΩSU(2). The essential reason for introducing hyperfunction theory is that the local contribution to the Duistermaat-Heckman polynomial near the image of a fixed point is a Green's function for an infinite order differential equation. Since infinite order differential operators do not act on Schwarz distributions, we are forced to use this more general theory.

Event Date: 
Tuesday, April 25, 2017 -
11:10 to 12:00
Voganish: A geometric approach to Arthur packets for p-adic groups

University of Maryland, Lie Groups and Representation Theory Seminar

Speaker: Clifton Cunningham

Title: Arthur packets packets for p-adic groups and vanishing cycles of perverse sheaves

Abstract: This talk will explain how to adapt the approach developed by Adams-Barbasch-Vogan to Arthur packets from Real groups to p-adic groups, and will illustrate this adaptation with several examples. We will also sketch a proof showing that Arthur packets are p-adic ABV packets for unipotent representations of p-adic special orthogonal groups.

Joint with: Bin Xu, Ahmed Moussaoui, Andrew Fiori, James Mracek

Event Date: 
Wednesday, March 29, 2017 -
14:00 to 15:00
Event Type: 

Lifts of Hilbert modular forms and application to a conjecture of Gross

Speaker: Lassina Dembélé, Max Planck Institut für Mathematik

Abstract: In this talk, we discuss the existence of certain lifts of Hilbert modular forms. We then use those lifts to provide theoretical evidence for a conjecture of Dick Gross on the modularity of abelian varieties not of GL_type.
(This is joint work with Clifton Cunningham.)

Location: MS 337 and

Event Date: 
Thursday, March 9, 2017 -
10:00 to 11:00
Event Type: 
Lifts of Hilbert modular forms and application to a conjecture of Gross

PIMS Focus Group on Representations in Arithmetic: Perfectoid spaces

Speaker: Kiran Kedlaya, University of California, San Diego (

Topic: Perfectoid spaces

Location: from UBC and on

More details on joining the lecture:

Notes from Prof. Kedlaya (and also part of the 2017 Arizona Winter School):

- Supplemented with background from Jared Weinstein's lecture notes:

This lecture series is part of the PIMS Focus Group on Representations in Arithmetic.

Event Date: 
Tuesday, February 21, 2017 -
16:00 to 17:15
Event Type: