Video Lectures

I will describe how the orbit method can be developed in a quantitative form, along the lines of microlocal analysis, and applied to local problems in representation theory and global problems involving the analysis of automorphic forms. This talk...

Understanding the complexity of the Minimum Circuit Size Problem (MCSP) is a longstanding mystery in theoretical computer science. Despite being a natural problem about circuits (given a Boolean function's truth table, determine the size of the...

In a work with Jacques Fejoz, we consider the conformal dynamics on a symplectic manifold , i.e. for which the symplectic form is transformed colinearly to itself. In the non-symplectic case, we study the problem of isotropy and uniqueness of...

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...