Video Lectures

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...

I will discuss compatibility of the canonical G-valued l-adic local systems on Shimura varieties of non-abelian type G. In previous work with Klevdal, we settled this for the projections of the local systems to the adjoint group of G, and this talk...

Gently stir a fluid in a large box sitting still. This talk is about the behavior of turbulence that is generated. We report results of large numerical simulations of the Navier-Stokes equations in a triply periodic box---and compare the outcomes...

The study of descriptive set theory in the context of determinacy axioms began nearly 60 years ago. The context for this study is now understood to be the Axiom AD+, which is a refinement of the Axiom of Determinacy (AD).  The objects of this study...

The development of set theory in the 20th century was like the invention of a "mathematical telescope", through which we can observe all kinds of infinite sets and their interactions. In quite the opposite direction, bounded arithmetic serves as a...

Projection theory asks how the size of a set in Rn—often measured by Hausdorff dimension—behaves under projections onto lower-dimensional spaces, both for orthogonal projections and for more general nonlinear families. One would like to understand...