Past Events

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...

In recent work, Haglund, Mason, van Willigenburg, and this author introduced a family of quasisymmetric functions which we call quasisymmetric Schur (QS) functions. These naturally refine the (symmetric) Schur functions and form a Z-basis of QSym...

This talk outlines multiscale problems which combine techniques of model reduction and filtering. Multiple time scales occur in models throughout the sciences and engineering, where the rates of change of different variables differ by orders of...

We introduce a 2x2 nonlinear nonlocal system. On the one hand, it models possible blow-up mechanism in the 3D Euler equations; On the other hand, it can be seen as a further step in the recent progress in understanding the role of nonlocal operators...