Video Lectures

A class of tensors, called "concise (m,m,m)-tensors  of minimal border rank", play an important role in proving upper bounds for the complexity of matrix multiplication. For that reason Problem 15.2 of "Algebraic Complexity Theory" by Bürgisser...

This colloquium will explore some fundamental issues in the mathematics of plasmas, focusing on the stability and instability of solutions to Vlasov-type equations, which are crucial for describing the behavior of charged particles in a plasma. A...

A dot-product proof is a simple probabilistic proof system in which the verifier decides whether to accept an input vector based on a single linear combination of the entries of the input and a proof vector. I will present constructions of linear...

Chapter 14 of the classic text "Computational Complexity" by Arora and Barak is titled "Circuit lower bounds: complexity theory's Waterloo". I will discuss the lower bound problem in the context of algebraic complexity where there are barriers...

The free group algebra appears often as a major tool in dealing with problems about free groups. It is also a lovely object for its own sake, featuring many analogies with the free group: for example, it satisfies an analog of the Nielsen-Schreier...

Artin groups are a family of groups generalizing braid groups, and are given by simple looking group presentations. In this talk, I will discuss profinite properties of Artin groups, such as residual finiteness, and the connection between the group...

The Poisson boundary is a measure theoretic object which classifies both the space of possible asymptotic events of a random walk and the space of bounded harmonic functions. For most identifications so far a moment condition has proved crucial. I...

A random walk on a hyperbolic group G will converge almost surely to the boundary, defining a stationary measure at infinity. When G is a cocompact fuchsian group, this boundary is the circle, and when the random walk is finitely supported it is...