Video Lectures

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...

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...