Past Events

A symplectic embedding of a disjoint union of balls into a symplectic manifold M is said to be of Kahler type if it is holomorphic with respect to some (not a priori fixed) integrable complex structure on M compatible with the symplectic form. I'll…

Abstract

In this talk, we strengthen a result by Ben Green on an analogue of Sárközy’s theorem in the setting of polynomial rings F_q[…

Shrinking Kähler-Ricci solitons model finite-time singularities of the Kähler-Ricci flow, hence the need for their classification. I will talk about the classification of such solitons in four real dimensions. This is joint work with Bamler-Cifarelli-Deruelle, Cifarelli-Deruelle, and Deruelle-…

Abstract

Problems on distribution of gaps between values of quadratic forms are among the most well-known open questions in number theory. In this talk, I will give an overview of some results on gaps between sums of two squares and discuss a connection between this area and theory of modular forms. More…

Khovanov homology extends to an invariant of smooth oriented 4-manifolds, which is defined as a skein module spanned by decorated embedded surfaces, modulo local relations. I will introduce equivariant and Lee versions of these skein modules and compute the latter. This leads to a non-vanishing…

We consider a continuous time simple random walk on a subset of the square lattice with wired boundary conditions: the walk transitions at unit edge rate on the graph obtained from the lattice closure of the subset by contracting the boundary into one vertex. We study the cover time of such walk…

Statistical mechanics models undergoing a phase transition often exhibit rich, fractal-like behavior at their critical points, which are described in part by critical exponents, the indices governing the power-law growth or decay of various quantities of interest. These exponents are…