Video Lectures

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...

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...

The Pila–Zannier strategy has proved to be a particularly fruitful approach: first applied to reprove the Manin–Mumford conjecture, it was later exploited decisively in proofs of the André–Oort conjecture. Crucially relying on a recent counting...