Video Lectures

I will discuss a recent notion - called categorical approximability - that extends the property of precompactness of a metric space. This is applied to certain spaces of Lagrangian submanifolds endowed with the spectral metric, such as exact...

This talk will recall the Birch--Swinnerton-Dyer Conjecture and describe highlights of the progress towards it, both pre- and post-millennium.  This will largely be a repeat of the speaker's plenary talk from the 2025 Clay Research conference on the...

What is the relative computational power of time and space? Tree evaluation (TreeEval) has become a central problem in understanding this question, especially after its application by Williams (STOC 2025, IAS CSDM seminar 9/23/25) to prove a...

I will discuss some recent work establishing the orderability of contact manifolds which arise as a quotient of an aspherically fillable manifold by a finite group action which extends (non-freely) to the filling. This generalizes the well known...

The local intertwining relation (LIR) is an identity that gives precise information about the action of normalized intertwining operators on parabolically induced representations. It plays a central role in Arthur’s endoscopic classification for...

Around 1921 Polya asked about the algebraicity of the indefinite integral of an algebraic function, in terms of the integrality of the coefficients in a power-series expansion. Polya nicely answered the special case of rational functions, using...

The generalized Markoff equation gives rise to a dynamical system via the Markoff group acting on the solution set. This talk considers the resulting dynamics over finite fields, which has strong connections with combinatorial group theory and...

The supercooled Stefan problem models how water, cooled below freezing, forms into ice. Experiments have shown that this process can exhibit nucleation (pieces of ice forming spontaneously) and that fractal-like patterns can emerge in the ice. This...

One of the fundamental problems in contact topology is to classify contact structures on a given 3-manifold. In particular, classifying contact structures on surgeries along a given knot has been very poorly studied. The only fully understood case...

Ever since Cohen invented forcing and showed the independence of the continuum hypothesis (CH), the powerset function of infinite cardinals has been a central theme in modern set theory. In this talk we will focus of the behavior of the powerset...