Past Events

Suppose you take a 1 x L strip of paper, twist it around in space, and tape the (short) ends together to make a paper Moebius band. In this talk I'll prove that you must have L > sqrt(3) and also that there is a unique limit that emerges if you have examples with L tending to sqrt(3). B.…

Abstract: Carleson proved in 1966 that the Fourier series of any square integrablefunction converges pointwise to the function, by establishing boundednessof the maximally modulated Hilbert transform from L^2 into weak L^2. Thistalk is about a generalization of his result, where the Hilbert…

Abstract: In 1980, Voiculescu introduced free probability theory, which lets us study non-commutative random variables, such as random matrices. In particular, in the free probability CLT the Gaussian limit is replaced by a semi-circular limit, which implies the semi-circular law. So far,…

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…