Video Lectures

We prove that the logarithm of Fourier series with random signs is integrable to any positive power. We use this result to prove the angular equidistribution of the zeros of entire functions with random signs (and more generally the almost sure...

I will survey what is known about the complexity of arithmetic circuits computing polynomials and rational functions with non-commuting variables, focusing on recent results and open problems. Strangely enough, some elementary questions in...

One of the most studied objects in mathematics is the modular curve, which is the quotient of hyperbolic 2-space by the action of \(\mathrm{SL}_2(\mathbb Z)\). It is naturally the home of modular forms, but it also admits an algebraic structure. The...

One of the key results in Robertson and Seymour's seminal work on graph minors is the Grid-Minor Theorem (also known as the Excluded Grid Theorem). The theorem states that any graph of treewidth at least \(k\) contains a grid minor of size \(f(k)\)...

The hyperbolic Ax Lindemann conjecture is a functional transcendental statement which describes the closure of "algebraic flows" on Shimura varieties. We will describe the proof of this conjecture and its consequences for the André-Oort conjecture...

I will describe several properties (structural and/or computational) which are satisfied by random matrices almost surely, but for which we have no concrete examples of such matrices. My hope is that the audience will be intrigued and interested in...

I will present recent results on a non-relativistic Hamiltonian model of quantum friction, about the motion of an invading heavy tracer particle in a Bose gas exhibiting Bose Einstein condensate. We prove the following observations: if the initial...

We review some of the connections, established and expected between random matrix theory and Zeta functions. We also discuss briefly some recent Universality Conjectures connected with families of L-functions.

Expanders are highly connected sparse graphs. Simplicial complexes are a natural generalization of graphs to higher dimension, and the notions of connectedness and expansion turn out to have interesting analogues, which relate to the homology and...