Video Lectures

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...

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...

Note: This talk will involve quantum computing, cryptography, and representation theory, but no background in any of these will be necessary to understand it. I'll introduce everything from the basics.

Aaronson, Atia, and Susskind (2020) established...

Let C be a closed surface and Σ⊂T*C a real exact Lagrangian surface associated to a spectral curve. In this talk we will first try to explain the context of this work (e.g., Higgs bundles and spectral curves). We then construct a homomorphism from...

Jacobi's theta function Θ(q):=1+2q+2q4+2q9+…, and more generally the theta functions associated to positive-definite quadratic forms, have the property that they are modular forms of half-integral weight. The usual proof of this fact is completely...