Geometric side of the trace formula and related problems

Geometric side of the trace formula and related problems - Ali Altuğ

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. In this talk I will give an overview of the problems (and partial solutions to some of them) for $\mathrm{GL}(2)$ and, maybe, discuss parts of the picture for (slightly more) general groups.