Past Events
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),…
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…
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…
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…
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…
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…
I will explain a nice characteristic class of SO(2n,C)SO(2n,\mathbf{C})SO(2n,C) bundles in both Chow cohomology and K-theory, and how to localise it to the zeros of an isotropic section. This builds on work of Edidin-Graham, Polishchuk-Vaintrob, Anderson and many others.
This can be used…