Video Lectures

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...

I will use a real-time general relativistic Black Hole Flight Simulator to show what really happens inside astronomically realistic black holes. The inner horizon of a rotating black hole is the most violent place in the Universe, easily reaching...

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...

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...