Past Events

Illusions have been a constant source of amusement but they are  also a unique gateway into understanding the way we perceive the world and how the brain processes information. Traditional visual illusions often involve a primary element—be it a line or a circle—that undergoes…

Einstein metrics and Ricci solitons are the fixed points of Ricci flow and model the singularities forming. They are also critical points of natural functionals in physics. Their stability in both contexts is a crucial question, since one should be able to perturb away from unstable models.

In this work, we establish a clear-cut criterion for determining when an affine subspace of R^n is extremal. Specifically, we investigate the behavior of the diophantine exponent of an affine subspace and determine when it is minimal (equal to the Dirichlet exponent 1/n). Our…

The large-scale rheology of random suspensions aims at describing how suspensions of small but many objects influence (sometimes drastically) a fluid flow. In physics this is the realm of complex fluids, with well-established phenomenological models. The derivation of such models from the…

Placing a two-dimensional lattice on another with a small rotation gives rise to periodic “moiré” patterns on a superlattice scale much larger than the original lattice.  The Bistritzer-MacDonald (BM) model attempts to capture the electronic properties of twisted bilayer graphene (TBG) by…

Knot Floer homology is a powerful link invariant. In its most general version, it is a bigraded chain complex over a polynomial ring F[U,V]. In this talk, I will describe the structure theorem of such objects - they are a direct sum of snake complexes and local systems - and explain what…

Abstract

Metric properties of harmonic measure is a perennial topic having much attention in the 80’ after works of Makarov, Jones, Wolff, Bourgain. However, certain questions of Peter Jones and Chris Bishop were left unsolved. Some of them concern free boundary problems for 1, 2, 3…

Abstract: The small quantum connection on a monotone symplectic manifold M is one of the simplest objects in enumerative geometry. Nevertheless, the poles of the connection have a very rich structure. After reviewing this background, I will outline a proof that, under suitable…

For many random graph models, the analysis of a related birth process suggests local sampling algorithms for the size of, e.g., the giant connected component, the k-core, the size and probability of an epidemic outbreak, etc. In this talk, I consider the question of when these algorithms are…