Video Lectures

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...

This public talk will be centered on John Cassidy's 2025 book, Capitalism and Its Critics, which provides a helpful framework for periods of economic disruption—like the one that AI seems likely to usher in.

John Cassidy has been a staff writer at Th...

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 emergence of mechanized Chinese writing in the nineteenth century and digital Chinese writing in the twentieth posed profound practical and conceptual challenges to a writing system whose history spans millennia. The dynamism, reach, and...

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...

"Wormholes" seem to describe ensemble averages of some kind, but in realistic models of holography, like AdS_4xS^7, it seems there isn't anything to average over, except, in some examples, a single integer N. Is "averaging over N" enough to account...

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...