Lecture Announcements
Date: Thursday, 31 July 2025
Time : Lecture 1 - 12.00 to 1.00 PM and Lecture 2 - 2.00 to 3.00 PM
Venue: LH202
Geometry of local Arthur packets and Vogan's conjecture for $p$-adic groups- I & II
Mishty Ray
University of British Columbia.
31-07-25

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Abstract

Local Arthur packets are sets of representations of p-adic groups that help us realize an important classes of automorphic representations. Vogan’s geometric perspective on the local Langlands correspondence establishes a bijection between equivalence classes of smooth irreducible representations of $G$, along with its pure inner forms, and simple equivariant perverse sheaves on a moduli space of Langlands parameters. This gives us the notion of an ABV-packet attached to a Langlands parameter. Conjecturally, ABV-packets are generalized A-packets; we call this Vogan's conjecture. In part I, we will set up the geometric perspective on the local Langlands correspondence with examples, and establish the statement of the main conjecture. In part II, we will report on the progress of the conjecture and sketch the main ingredients of the proof in the case of general linear groups and odd special orthogonal groups.