Video Lectures

I will discuss work in progress developing the theory of log prismatic cohomology and related theories using the Cartier-Witt stack.  

We ask the question, “how does the infinite q-Pochhammer symbol transform under modular transformations?” and connect the answer to that question to the Stark conjectures. The infinite q-Pochhammer symbol transforms by a generalized factor of...

I will discuss infinite-dimensional linear programs producing bounds on the spectral gap in various settings. This includes new bounds on the spectral gap of hyperbolic manifolds as well as the Cohn+Elkies bound on the density of sphere packings...

In this talk, we introduce the analytic de Rham stack for rigid varieties over Qp

 (and more general analytic stacks). This object is an analytic incarnation of the (algebraic) de Rham stack of Simpson, and encodes a theory of analytic D-modules...

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...