Past Events

Abstract: A Morse function f on a manifold M is called strong if all its critical points have different critical values. Given a strong Morse function f and a field F we construct a bunch of elements of F, which we call Bruhat numbers (they're defined up to sign). More concretely,…

Abstract:

We will discuss a graph that encodes the divisibility properties of integers by primes. We show that this graph is shown to have a strong local expander property almost everywhere. We then obtain several consequences in number theory, beyond the traditional parity…

For X of “classical Lie type” (formally such that X has a GKM torus action where all characters are of the form t_i, t_i+t_j, and t_i-t_j for various i,j), we adapt for combinatorial applications the (equivariant) Hirzebruch-Riemann-Roch framework which computes Euler characteristics of vector…

Is it possible to give an algebraic description of the set of locally flat discs with boundary a fixed knot K up to isotopy rel boundary? Working in the topological category, this talk will describe progress towards this question assuming some conditions on the…

Motivated by mirror symmetry and the enumeration of curves with boundaries, it is desirable to develop a theory of Gromov-Witten invariants in the setting of non-archimedean geometry. I will explain our recent works in this direction. Our approach differs from the classical one in algebraic…

In this talk, I will describe my recent joint work with Robert Haslhofer on uniqueness and non-uniqueness of ancient ovals under mean curvature flow.  We confirm the conjecture of Angenent-Daskalopoulos-Sesum that $SO(k)\times SO(n+1-k)$-symmetric ancient ovals are unique up to…

Abstract: We employ separation of variables to prove weighted resolvent estimates for the semiclassical Schrödinger operator $-h^2 \Delta + V(|x|) - E$  in dimension $n \ge 2$, where, $h, \, E > 0$ and $V : [0, \infty) \to \mathbb{R}$ is $L^\infty$ …

Picture $n$ particles arranged into "blobs" (a partition of $n$). Each time, a pair of particles is randomly chosen. If they are in the same blob, the blob breaks into two (uniformly). If they are in different blobs, the blobs merge. Natural questions arise: What is the stationary distribution?…