Video Lectures

I will discuss new constraints on the spectra of Maass forms on compact hyperbolic 2-orbifolds. The constraints arise from integrals of products of four functions in discrete series representations realized in L2(Γ∖G), where Γ is a cocompact lattice...

A landmark result of Ratner states that if G is a Lie group, Γ a lattice in G and if ut is a one-parameter Ad-unipotent subgroup of G, then for any x∈G/Γ the orbit ut.x is equidistributed in a periodic orbit of some subgroup L less than G, and...

The talk will be devoted to explain how to construct weak solutions to 3D Ideal MHD equations obtained by convex integration (in the non smooth regime). We will show the existence of bounded weak solutions dissipating energy and cross helicity but...

I will present a joint work with Lijie, in which we revise the hardness vs randomness framework so that it can work in a non-black-box fashion. That is, we construct derandomization algorithms that do not rely on classical PRGs, and instead "extract...

If G is a Lie group whose adjoint representation preserves a nondegenerate symmetric bilinear form on its Lie algebra (e.g. a semisimple group) and F is the fundamental group of a closed oriented surface S, then the spaces of equivalence classes of...

Let X be a smooth affine algebraic variety over the field C of complex numbers (that is, a smooth submanifold of C^n which can be described as the solutions to a system of polynomial equations). Grothendieck showed that the de Rham cohomology of X...

I'll present a new algorithm to refute, that is, efficiently find certificates of unsatisfiability, for smoothed instances of k-SAT and other CSPs. Smoothed instances are produced by starting with a worst-case instance and flipping each literal in...

In this talk I will introduce barcode entropy and discuss its connections to topological entropy. The barcode entropy is a Floer-theoretic invariant of a compactly supported Hamiltonian diffeomorphism, measuring, roughly speaking, the exponential...

High-eccentricity migration is a possible formation channel for hot Jupiters. However, in order for it to be consistent with the observed population of planets, tides must circularize the orbits in an efficient manner. In this talk, I will discuss...

I will present results on Glauber dynamics of Ising models and continuum

φ4 measures.

For ferromagnetic Ising models, we show that the log-Sobolev constant satisfies a simple bound expressed only in terms of the susceptibility of the model...