School of Mathematics

Motivic correlators and locally symmetric spaces

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.

Elementary open problems in Algebra (with consequences in computational complexity)

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.