Geometric side of the trace formula and related problems

Ali Altuğ
Massachusetts Institute of Technology
September 30, 2016
A general problem in Beyond Endoscopy is to understand the terms on the geometric side of the trace formula and to get enough control on their Fourier (or related) transforms. The problem itself has several different ingredients with different flavors (some local some global, for instance) like the singularities of orbital integrals, irregular variation of class numbers of tori in families, contributions of non-tempered representations etc.

Decomposing symmetric powers

Bill Casselman
University of British Columbia
September 30, 2016
One problem raised recently by Langlands in connection with the trace formula was the decomposition of symmetric powers of irreducible representations of $\mathrm{GL}(2)$. There is a classical formula for this. I shall explain a new version of this formula and, with luck, describe computer experiments examining the extent to which the idea will work for other groups.

Regular supercuspidal representations

Tasho Kaletha
University of Michigan
October 1, 2016
Jiu-Kang Yu has given a general construction of supercuspidal representations of tamely ramified reductive p-adic groups. We will show that most of these representations can be parameterized by conjugacy classes of pairs consisting of an elliptic maximal torus and a character of it, subject to a simple and explicit root-theoretic condition. We will then draw a remarkable parallel between the characters of these representations and the characters of discrete series representations of real reductive groups.