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...

For a quantum field of arbitrary mass and spin in the static patch of de Sitter spacetime, the Euclidean partition function receives contributions from edge modes localized on the horizon, expressible in terms of the Harish-Chandra character of the...

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...

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...