Video Lectures

Certain `flexible' structures in symplectic and contact topology satisfy h-principles, meaning that their geometry reduces to underlying topological data. Although these flexible structures have no interesting geometry by themselves, I will show how...

The theory of complex multiplication describes finite abelian extensions of imaginary quadratic number fields using singular moduli, which are special values of modular functions at CM points. I will describe joint work with Henri Darmon in the...

In this talk, I will give an overview of some of what is known about solutions to the thin obstacle problem, and then move on to a discussion of a higher regularity result on the singular part of the free boundary. This is joint work with Xavier...

In recent works with N. Wickramasekera we develop a regularity and compactness theory for stable hypersurfaces (technically, integral varifolds) whose generalized mean curvature is prescribed by a (smooth enough) function on the ambient Riemannian...

Invariant theory is a fundamental subject in mathematics, and is potentially applicable whenever there is symmetry at hand (group actions). In recent years, new problems and conjectures inspired by complexity have come to light. In this talk, I will...

We give a pseudorandom generator that fools $m$-facet polytopes over $\{0,1\}^n$ with seed length $\mathrm{polylog}(m) \cdot \mathrm{log}(n)$. The previous best seed length had superlinear dependence on $m$. An immediate consequence is a...

Abstract: I will survey (in)coherence of lattices in semisimple Lie groups, with a view toward open problems and connections with the geometry of locally symmetric spaces. Particular focus will be placed on rank one lattices, where I will discuss...