Previous Conferences & Workshops

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...

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...

Organizers: Nima Arkani-Hamed, June Huh, Thomas Lam, and Bernd Sturmfels

This event aimed to foster collaboration between mathematicians and physicists. The focus was on the intersection of combinatorial geometry and fundamental physics, covering...

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...

The outer automorphism group of the free group Out(F_r) acts as the isometry group on the deformation space of weighted graphs, Culler-Vogtmann Outer space CV_r. The train track theory of Bestvina-Feighn-Handel bridges studying topological...