Wavefront Sets in Number Theory and Representation Theory

(13 Sep 2027–24 Sep 2027)

Organizing Committee

 

Co-chairs

 
 

Overview

This program centers on the theory of wavefront sets and related microlocal invariants in the representation theory of reductive groups, with particular emphasis on their geometric structure and arithmetic significance.

The wavefront set is a fundamental invariant of a representation, encoding deep properties such as unitarity and reducibility. Originally studied through its connection with local character expansions, it now lies at the intersection of several major developments in modern representation theory, including the theta correspondence, the orbit method, the classification of unipotent representations, and emerging microlocal approaches to Arthur packets.

The program aims to advance the understanding of wavefront sets by exploring their connections with geometric and representation-theoretic invariants, consolidating recent computational and theoretical developments, and deepening their links with arithmetic invariants, Galois representations, and L-functions.

Activities

Week 1: Minicourses and Early-Career Talks (Monday–Friday)
Format: 3–5 minicourses (approximately 3 hours each), complemented by talks by early-career researchers to encourage interaction across career stages.

Week 2: International Conference (Monday–Friday)
Format: Conference talks organized around the program’s main themes, including:

  • Computational and Theoretical Advances: Germ expansions, orbital integrals, degenerate Whittaker models, asymptotic cones, local branching laws, and connections with geometric invariant theory
  • Unipotent Representations and Theta Correspondence: Geometric and analytic constructions of unipotent representations and their singular support
  • Langlands and Galois Aspects: Connections with the Langlands program, arithmetic wavefront sets, and Arthur packets
  • Microlocal and Geometric Approaches: Relative Langlands duality, perverse sheaves, and Hamiltonian geometry
  • Modular Aspects: Gelfand–Kirillov dimension over general coefficient rings and mod (p) representation theory
DateAbstract
Week 1: Minicourses and Early-Career Talks 13–17 Sep 2027N/A
Week 2: International Conference 20–24 Sep 2027N/A
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