## An introduction to Dolgopyat's method

Frédéric Naud

Université Avignon

October 11, 2017

Frédéric Naud

Université Avignon

October 11, 2017

Semyon Dyatlov

Massachusetts Institute of Technology

October 11, 2017

Michael Magee

Durham University

October 11, 2017

Semyon Dyatlov

Massachusetts Institute of Technology

October 10, 2017

Ankit Garg

Microsoft Research

October 10, 2017

Invariant theory studies the actions of groups on vector spaces and what polynomial functions remain invariant under these actions. An important object related to a group action is the null cone, which is the set of common zeroes of all homogeneous invariant polynomials. I will talk about the structural aspects of the null cone from a computational and optimization perspective. These will include the Hilbert-Mumford and Kempf-Ness theorems which imply that null cone membership is in NP intersect coNP (ignoring bit-size issues).

Ruixiang Zhang

Member, School of Mathematics

October 10, 2017

Yiannis Sakellaridis

Rutgers University; von Neumann Fellow, School of Mathematics

October 10, 2017

"Beyond endoscopy", broadly interpreted, is the idea that functoriality should be realized as a comparison between stable trace formulas. The nature of this comparison, however, remains completely unclear.

Long Jin

Purdue University

October 10, 2017

Stéphane Nonnemacher

Université Paris-Sud

October 9, 2017

Akshay Venkatesh

Stanford University; Distinguished Visiting Professor, School of Mathematics

October 9, 2017

Locally symmetric spaces are a class of Riemannian manifolds which play a special role in number theory. In this talk, I will introduce these spaces through example, and show some of their unusual properties from the point of view of both analysis and topology. I will conclude by discussing their (still very mysterious) relationship with algebraic geometry.