Video Lectures

Can we reconstruct a function by knowing only a subset of its values and a subset of the values of the function's Fourier transform?

How many values do we need to know for such a reconstruction? Can we interpolate a given subset of values? What are...

I will explain what the question means and how to make it precise. Then I will give a conjectural answer. This is based on joint work with Peter Scholze.

The theory of matroids provides a unified abstract treatment of the concept of dependence in linear algebra and graph theory. In this talk we explain Bergman fans of matroids, and we investigate isomorphisms of Bergman fans for different fan...

A compact invariant set of a flow is called locally maximal when it is the largest invariant set in some neighborhood. In this talk, based on joint work with Erman Cineli, Viktor Ginzburg, and Basak Gurel, I will present a "forced existence" result...

Homological stability is now well established as an organizing principle and computational tool in algebraic topology and other areas. In many cases it is of interest to obtain homological stability with twisted coefficients, and the standard choice...

This talk is a discussion about the extremal points of the unit ball with respect to the Hessian-Schatten variation seminorm, i.e. the total variation of the second distributional differential with respect to the Schatten matrix norm. The main...

Spectral invariants defined via Embedded Contact Homology (ECH) or the closely related Periodic Floer Homology (PFH) satisfy a Weyl law: Asymptotically, they recover symplectic volume. This Weyl law has led to striking applications in dynamics...

This is a report of joint work with Bergström-Diaconu-Westerland and Miller-Patzt-Randal-Williams.

Based on random matrix theory, Conrey-Farmer-Keating-Rubinstein-Snaith have conjectured precise asymptotics for moments of families of quadratic L...

The braid group B_{2g+1} has a description in terms of the hyperelliptic mapping class group of a curve X of genus g.  This equips it with an action on V = H_1(X), and we may produce a wealth of new representations S^{\lambda}(V) by applying Schur...

A basic question in arithmetic statistics is:  what does the Selmer group of a random abelian variety look like?  This question is governed by the Poonen-Rains heuristics, later generalized by Bhargava-Kane-Lenstra-Poonen-Rains, which predict, for...