Beyond Endoscopy

Beyond Endoscopy is the proposal by Langlands for using the trace formula to attack the Principle of Functoriality. Many of the problems at this (early) stage concern the geometric terms in the trace formula. Most immediate perhaps is to extend...

Asymptotics for the distribution of Hecke eigenvalues in families of automorphic forms are useful to study families of L-functions, provided one has a sufficiently good estimate for the error term of the asymptotic. I want to present ongoing joint...

This is a survey of how the existing theories of L-functions are in agreement with Braverman-Kazhdan/Ngo's construction of L-functions which generalizes that of Godement-Jacquet. One hopes that such insights may play a role in understanding the...

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...

Lecture notes: http://publications.ias.edu/sites/default/files/80th_0.pdf

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...

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...

Lecture notes: http://publications.ias.edu/sites/default/files/80th_0.pdf