Upcoming Events
Abstract: I will talk about a recent result that any sufficiently nice even analytic function can be recovered from its values at the nontrivial zeros of zeta(1/2+is) and the values of its Fourier transform at logarithms of positive integers. The proof is based on an explicit interpolation…
The Ax-Grothendieck theorem states that every injective polynomial from C^n to C^n is bijective. I'll "prove" this theorem using model theory. Along the way, we'll take a brief tour of some important but surprisingly accessible theorems related to first-order logic. I won't assume any previous…
A general belief is that exact Lagrangian fillings can be distinguished using cluster theory. In this talk, I will present such a framework via Floer theory — given a positive braid Legendrian link, its augmentation variety is a cluster K_2 variety and its admissible fillings induce cluster…
It is well known that the genus g of a knot is the highest Alexander grading for which the knot Floer homology is nontrivial. In recent years, there is evidence suggesting that the knot Floer homology is also nontrivial in the Alexander grading g-1. In this talk, I will describe a proof that the…
I will discuss some simplified models for the shape of liquid droplets on rough solid surfaces. These are elliptic free boundary problems with oscillatory coefficients. I will talk about the large scale effects of small scale surface roughness, e.g. contact line pinning, hysteresis, and…
It has been a classical question which manifolds admit Riemannian metrics with positive scalar curvature. I will present some recent progress on this question, ruling out positive scalar curvature on closed aspherical manifolds of dimensions 4 and 5 (as conjectured by Schoen-Yau and by Gromov),…
Abstract: The Teukolsky equation is one of the fundamental equations governing linear gravitational perturbations of the Kerr black hole family. We study fixed frequency solutions and obtain estimates which are uniform in the frequency parameters. Due to the separability of the Teukolsky…
Abstract: I will discuss recent work calculating the top weight cohomology of the moduli space $A_g$ of principally polarized abelian varieties of dimension $g$ for small values of $g$. The key idea is that this piece of cohomology is encoded combinatorially via the…