Video Lectures

The study of nodal sets of Laplace eigenfunctions has intrigued many mathematicians over the years. The nodal count problem has its origins in the works of Strum (1936) and Courant (1923) which led to questions that remained open to this day. One...

Several well-known open questions, such as: "are all groups sofic or hyperlinear?", have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in...

In this talk I will introduce constructions of finite graphs which resemble some given infinite graph both in terms of their local neighborhoods, and also their spectrum. These graphs can be thought of as expander graphs with local constraints in a...

Motivated by thematic similarities between persistent homology and magnitude homology, we describe a simplicial construction associated to a metric space. This construction is determined by (apart from the metric space itself) a choice of two...

The Arnold conjecture about fixed points of Hamiltonian diffeomorphisms was partly motivated by the celebrated Poincare-Birkhoff fixed point theorem for an area-preserving homeomorphism of an annulus in the plane. Despite the fact that the Arnold...

The Langlands program is a far-reaching collection of conjectures that relate different areas of mathematics including number theory and representation theory. A fundamental problem on the representation theory side of the Langlands program is the...

Diagonalization is incredibly important in every field of mathematics. I am a representation theorist, so I will start by motivating the uses of diagonalization in representation theory. Then comes a brief introduction to categorical representation...

It is known that any opened necklace with beads of n types can be partitioned by at most (k-1)n cuts into intervals that can be distributed into k collections, each containing the same number of beads of each type (up to 1). The proof is topological...