Past Events

In this talk we outline the main ideas that come upon the computation of quotients of tori by actions of Z/p induced by linear representations of Z/p. These are called toroidal orbifolds. The talk will be aimed to a general audience. This is joint...

At certain special points, the values of the Riemann zeta function and many other L-functions are algebraic, up to a well-determined transcendental factor. G. Shimura, H. Maass, and M. Harris extensively studied a class of differential operators on...

According to the Birch and Swinnerton-Dyer conjecture, the order of the Tate-Shafarevich group can be expressed as the ratio of several invariants of the curve. However, this ratio involves two numbers which are expected to be irrational; namely $L^{...

I will speak about the cohomology of the middle degree of graph hypersurfaces of some special Feynman graphs, the "generalised zigzag" graphs, and about how to connect this to counting rational points of this hypersurfaces. Then I will explain, why...

I will survey some recent results on several types of aggregation equations. These are continuum models used to describe the swarming phenomenon in biology. I will focus on mathematical issues related to the basic understanding of these equations...

The braid group has a left-invariant total ordering, called the Dehornoy ordering. In this talk, I will introduce the Dehornoy floor of braids, which measures a complexity of braids by using the Dehornoy ordering. I will give a new lower bound of...

Regarding his 1920 paper proving recurrence of random walks in Z^2, Polya wrote that his motivation was to determine whether 2 independent random walks in Z^2 meet infinitely often. Of course, in this case, the problem reduces to the recurrence of a...

I will describe a new operad (the "splicing operad") that acts on a fairly broad class of embedding spaces. Previously I constructed an action of the operad of little (j+1)-cubes on the space of framed long embeddings of R^j in R^n. This operad...

I will explain recent joint work with Xiaoyi Zhang on threshold solutions to critical nonlinear Schrodinger equations. These results are analogues of Liouville-type theorems in the dispersive setting. I will cover mainly the mass-critical case. Time...