## Harmonic Analysis and the Trace Formula, Mathematisches Forschungsinstitut Oberwolfach (MFO)

Title: Arthur packets and Adams-Barbash-Vogan packets for p-adic groups

Speakers: Bin Xu and Clifton Cunningham

## Harmonic Analysis and the Trace Formula, Mathematisches Forschungsinstitut Oberwolfach (MFO)Title: Arthur packets and Adams-Barbash-Vogan packets for p-adic groups Speakers: Bin Xu and Clifton Cunningham Event Date: Wednesday, May 24, 2017 - 11:30 to 12:30 Event Type: Project: Voganish |

## James Mracek thesis defence, Part 1Title: Applications of algebraic microlocal analysis in symplectic geometry and representation theory 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. 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 p-adic groups |

## University of Maryland, Lie Groups and Representation Theory SeminarSpeaker: 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 https://www-math.umd.edu/research/seminars/lie-groups-and-rep-theory-sem... Event Date: Wednesday, March 29, 2017 - 14:00 to 15:00 Event Type: |

## Lifts of Hilbert modular forms and application to a conjecture of GrossSpeaker: 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. Location: MS 337 and https://zoom.us/j/344804314 Event Date: Thursday, March 9, 2017 - 10:00 to 11:00 Event Type: Project: Lifts of Hilbert modular forms and application to a conjecture of Gross |

## Voganish SeminarUpdate on the paper. Event Date: Thursday, March 2, 2017 - 10:00 to 12:00 Event Type: |

## PIMS Focus Group on Representations in Arithmetic: Perfectoid spacesSpeaker: Kiran Kedlaya, University of California, San Diego (http://www.kskedlaya.org/) Topic: Perfectoid spaces Location: from UBC and on https://bluejeans.com/211681494/browser More details on joining the lecture: http://www.pims.math.ca/scientific-event/170220-rakk Notes from Prof. Kedlaya (and also part of the 2017 Arizona Winter School): - https://cloud.sagemath.com/projects/7da27120-4e06-4340-bbcb-70054d89ac67... 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: |

## PIMS Focus Group on Representations in Arithmetic: Adic SpacesSpeaker: Kiran Kedlaya, University of California, San Diego (http://www.kskedlaya.org/) Topic: Adic spaces Location: from UBC and on https://bluejeans.com/211681494/browser More details on joining the lecture: http://www.pims.math.ca/scientific-event/170220-rakk Notes from Prof. Kedlaya (and also part of the 2017 Arizona Winter School): - https://cloud.sagemath.com/projects/7da27120-4e06-4340-bbcb-70054d89ac67... This lecture series is part of the PIMS Focus Group on Representations in Arithmetic. Event Date: Monday, February 20, 2017 - 14:00 to 15:00 Event Type: |

## Voganish Seminar: pure inner formsSpeakers: Ahmed, Bin and Clifton. Topic: Review Arthur's main local result in the endoscopic classification, adapted to pure inner twists of quasi-split classical p-adic 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 Event Type: |

## UBC Number Theory Seminarhttp://www.pims.math.ca/scientific-event/170209-ntsgkft Speaker: Kam-Fai Tam Location: University of British Columbia, Room ESB 4127 Part I: Representations of reductive groups over local fields Part II: Endoscopic classification of essentially tame supercuspidal representations for quasi-split classical groups Event Date: Thursday, February 9, 2017 - 15:30 to 16:30 Event Type: |

## Abelian Varieties Seminarhttps://www.pims.math.ca/scientific-event/170209-avmsssja 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) Abel-Jacobi 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 Casalaina-Martin and Charles Vial.) A video of this event is available on mathtube.org (http://www.mathtube.org/lecture/video/distinguished-models-intermediate-...). Location: Video from Colorado State University Event Date: Thursday, February 9, 2017 - 12:00 to 13:00 Event Type: |

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