Video Lectures

Expander graphs are graphs which simultaneously are both sparse and highly connected. The theory of expander graphs received a lot of attention in the past half a century, from both computer science and mathematics. In recent years, a new theory of...

We will discuss the mean curvature flow of nn-dimensional submanifolds in ℝn+kRn+k satisfying a pinching condition |A|2

A 1948 theorem of de Bruijn and Erdős says that if nn points in a projective plane do not lie all on a line, then they determine at least n lines. More generally, Dowling and Wilson conjectured in 1974 that for any finite set of vectors spanning a...

Non-constructive existence proofs, which establish the existence of objects without furnishing an efficient algorithm to produce examples, abound in mathematics. How hard is it, computationally, to find objects whose existence is guaranteed non...

The purpose of this talk is to explore how Lagrangian Floer homology groups change under (non-Hamiltonian) symplectic isotopies on a (negatively) monotone symplectic manifold (M,ω)(M,ω) satisfying a strong non-degeneracy condition. More precisely...

The talk covers Chapter 6 in Jantzen's book.

In the upcoming series of talks we discuss some equivalences by Bezrukavnikov between categories of coherent sheaves on Steinberg varieties and of perverse sheaves on the affine flag variety. In this talk I discuss the decategorified isomorphism...

A recent result of Becker, Lubotzky and Thom characterizes, for amenable groups, permutation stability in terms of co-soficity of invariant random subgroups (IRS). We will explain that for a class of amenable groups acting on rooted trees, including...

A polynomial with nonnegative coefficients is strongly log-concave if it and all of its derivatives are log-concave as functions on the positive orthant. This rich class of polynomials includes many interesting examples, such as homogeneous real...

Our study is motivated by earlier results about nodal count of Laplacian eigenfunctions on manifolds and graphs that share the same flavor: a normalized nodal count is equal to the Morse index of a certain energy functional at the critical point...