## Transversality for coproduct and cobracket

Dingyu Yang

Member, School of Mathematics

September 28, 2016

Dingyu Yang

Member, School of Mathematics

September 28, 2016

Jingyu Zhao

Member, School of Mathematics

September 28, 2016

Jean Bourgain

IBM von Neumann Professor, School of Mathematics

September 29, 2016

Ngô Bảo Châu

University of Chicago

September 30, 2016

Robert Langlands

Professor Emeritus, School of Mathematics

September 30, 2016

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

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.

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.

Robert Langlands

Professor Emeritus, School of Mathematics

September 30, 2016

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

Ngô Bảo Châu

University of Chicago

October 1, 2016

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.