Video Lectures

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...

I will describe a large ensemble of compactifications of type IIB string theory on Calabi-Yau threefold hypersurfaces, obtained by triangulating polytopes from the Kreuzer-Skarke list. We have developed methods to compute effective theories in the...

I will explain a polyfold proof, joint with Katrin Wehrheim, of the Arnold conjecture: the number of 1-periodic orbits of a nondegenerate 1-periodic Hamiltonian on a closed symplectic manifold is at least the sum of the Betti numbers. Our proof is a...

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...

I will present a proof with some substantial details of the Multiplicity One Conjecture in Min-max theory, raised by Marques and Neves. It says that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal...

Abstract: There seems to be an analogy between the classes of fundamental groups of compact 3-manifolds and of one-relator groups.  (Indeed, many 3-manifold groups are also one-relator groups.) For instance, Dehn’s Lemma for 3-manifolds (proved by...

In this talk, we will be concerned with the existence of a third embedded minimal hypersurface spanning a closed submanifold B contained in the boundary of a compact Riemannian manifold with convex boundary, when it is known a priori the existence...