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: http://blog.math.toronto.edu/GraduateBlog/files/2017/01/utthesis002.pdf
Institution: University of Toronto
PhD Advisors: Lisa Jeffrey – Clifton Cunningham
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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 padic 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 Dmodules 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 padic 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 DuistermaatHeckman function for a Hamiltonian action of a compact torus on an infinite dimensional symplectic manifold. We show that the DuistermaatHeckman 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 DuistermaatHeckman 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.
https://seminars.math.toronto.edu/seminars/list/events.py/process?action...
Event Date: Tuesday, April 25, 2017  11:10 to 12:00 Project: Voganish: A geometric approach to Arthur packets for padic groups

Speaker: Clifton Cunningham
Title: Arthur packets packets for padic groups and vanishing cycles of perverse sheaves
Abstract: This talk will explain how to adapt the approach developed by AdamsBarbaschVogan to Arthur packets from Real groups to padic groups, and will illustrate this adaptation with several examples. We will also sketch a proof showing that Arthur packets are padic ABV packets for unipotent representations of padic special orthogonal groups.
Joint with: Bin Xu, Ahmed Moussaoui, Andrew Fiori, James Mracek
https://wwwmath.umd.edu/research/seminars/liegroupsandreptheorysem...
Event Date: Wednesday, March 29, 2017  14:00 to 15:00

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 https://zoom.us/j/344804314
Event Date: Thursday, March 9, 2017  10:00 to 11:00 Project: Lifts of Hilbert modular forms and application to a conjecture of Gross

Event Date: Thursday, March 2, 2017  10:00 to 12:00

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

Event Date: Monday, February 20, 2017  14:00 to 15:00

Speakers: Ahmed, Bin and Clifton.
Topic: Review Arthur's main local result in the endoscopic classification, adapted to pure inner twists of quasisplit classical padic groups (Conjecture 9.4.2 in Arthur's book). Also review Kaletha's notion of rigid inner twists. We need this to state Voganish Conjecture 1, properly.
Location: Bin and Clifton at the University of Calgary, Room MS 337, Ahmed in Paris, and on https://zoom.us/j/525655184
Event Date: Thursday, February 16, 2017  09:00 to 11:00

http://www.pims.math.ca/scientificevent/170209ntsgkft
Speaker: KamFai Tam
Location: University of British Columbia, Room ESB 4127
Part I: Representations of reductive groups over local fields
In this talk, we describe the representations of certain reductive groups over local fields and the representations of Weil groups. Then we review the class field theory for local fields and the Langlands correspondence for these reductive groups. The talk will be a brief overview of the representation theory of reductive groups over local fields, largely based on examples of lowrank groups.
Part II: Endoscopic classification of essentially tame supercuspidal representations for quasisplit classical groups
Continue from the last talk, we specify our reductive group \mathbf{G} to be a quasisplit classical group (special orthogonal, symplectic, unitary) over a padic field of odd residual characteristic. We describe the endoscopic classification, proved by Arthur and Mok, of certain supercuspidal representations and their Lpackets of \mathbf{G}, under some regularity and tameness conditions. These representations can be described by inducing types constructed by BushnellKutzko, Stevens, or Yu, and they correspond to Langlands parameters related to characters of elliptic maximal tori of \mathbf{G}.
(This work is partly joint with Corinne Blondel.)
Event Date: Thursday, February 9, 2017  15:30 to 16:30

https://www.pims.math.ca/scientificevent/170209avmsssja
Speaker: Jeffrey Achter
Title: Distinguished models of intermediate Jacobians
Abstract: Consider a smooth projective variety over a number field. The image of the associated (complex) AbelJacobi map inside the (transcendental) intermediate Jacobian is a complex abelian variety. We show that this abelian variety admits a distinguished model over the original number field, and use it to address a problem of Mazur on modeling the cohomology of an arbitrary smooth projective variety by that of an abelian variety. (This is joint work with Sebastian CasalainaMartin and Charles Vial.)
A video of this event is available on mathtube.org (http://www.mathtube.org/lecture/video/distinguishedmodelsintermediate...).
Location: Video from Colorado State University
Event Date: Thursday, February 9, 2017  12:00 to 13:00

James and Ahmed: inertial classes and the Bernstein decomposition from the Voganish perspective.
Location: James at the University of Toronto, Ahmed in Paris, and on https://zoom.us/j/344804314
Event Date: Thursday, February 9, 2017  09:00 to 11:00
