## Categorical actions in geometry and representation theory

Clemens Koppensteiner

Member, School of Mathematics

September 29, 2017

Clemens Koppensteiner

Member, School of Mathematics

September 29, 2017

Pravesh Kothari

Member, School of Mathematics

September 29, 2017

Omri Weinstein

Columbia University

October 2, 2017

This paper proves the first super-logarithmic lower bounds on the cell-probe complexity of dynamic boolean (a.k.a. decision) data structure problems, a long-standing milestone in data structure lower bounds.

Bao V. Le Hung

Member, School of Mathematics

October 2, 2017

Marius Lemm

Member, School of Mathematics

October 2, 2017

Sara Tukachinsky

Member, School of Mathematics

October 2, 2017

Zheng Liu

Member, School of Mathematics

October 2, 2017

James Maynard

Member, School of Mathematics

October 2, 2017

Avi Wigderson

Herbert H. Maass Professor, School of Mathematics

October 3, 2017

I will survey some elementary (to state!) problems on groups, matrices, and tensors, and discuss their motivations arising from several major problems in computational complexity theory. On each problem there was some exciting recent progress which may raise hope it can be resolved. No special background will be assumed.

Alexander Goncharov

Yale University; Member, School of Mathematics and Natural Sciences

October 3, 2017

According to Langlands, pure motives are related to a certain class of automorphic representations.

Can one see mixed motives in the automorphic set-up? For examples, can one see periods of mixed motives in entirely automorphic terms? The goal of this and the next lecture is to supply some examples.

We define motivic correlators describing the structure of the motivic fundamental group $\pi_1^{\mathcal M}(X)$ of a curve. Their relevance to the questions raised above is explained by the following examples.