Video Lectures

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...

Abstract: This will be a broad talk about coherence of groups, and how it relates to conjectures about hyperbolic groups with planar boundaries. A group is coherent if every finitely generated subgroup is finitely presented.  This is a property...

Kazhdan–Lusztig (KL) polynomials for Coxeter groups were introduced in the 1970s, providing deep relationships among representation theory, geometry, and combinatorics. In 2016, Elias, Proudfoot, and Wakefield defined analogous polynomials in the...

In the early 1930's, the Ergodic theorems of von Neumann and Birkhoff put Boltzmann's Ergodic Hypothesis in mathematical terms, and the natural question was born: is ergodicity the "general case" among conservative dynamical systems? Oxtoby and Ulam...