Video Lectures

Donaldson-Thomas (DT) invariants of a quiver with potential can be expressed in terms of simpler attractor DT invariants by a universal formula. The coefficients in this formula are calculated combinatorially using attractor flow trees. In joint...

This lecture is devoted to a survey on explicit stability results in Gagliardo-Nirenberg-Sobolev and logarithmic Sobolev inequalities. Generalized entropy methods based on carré du champ computations and nonlinear diffusion flows can be used for...

In 1996 Manjul Barghava introduced a notion of P-orderings for arbitrary sets S of a Dedekind domain, with respect to a prime ideal P, which defined associated invariants called P-sequences. He combined these invariants to define generalized...

The Lipschitz extension problem is the following basic “meta question” in metric geometry:  Suppose that X and Y are metric spaces and A is a subset of X. What is the smallest K such that every Lipschitz function f:A\to Y has an extension F:X\to Y...

How do we describe the topology of the space of all nonconstant holomorphic (respectively, algebraic) maps F: X--- greater than Y  from one complex manifold (respectively, variety) to another? What is, for example, its cohomology? Such problems are...

A CSS quantum code C=(W1,W2) is a pair of orthogonal subspaces in 𝔽n2. The distance of C is the smallest hamming weight of a vector in W⊥1−W2 or W⊥2−W1. A large distance roughly means that the quantum code can correct many errors that affect the...

Hives, as defined by Knutson and Tao, are discrete concave functions on a triangular grid on an equilateral triangle of side n. It is known through the work of Knutson and Tao that the probability distribution of the spectrum of the sum of two...

We consider the Schramm-Loewner evolution (SLE_{kappa}) for kappa in (4,8), which is the regime that the curve is self-intersecting but not space-filling. We let K be the set of kappa in (4,8) for which the adjacency graph of connected components of...

We prove this bound by first using the unitary Ichino-Ikeda formula of N. Harris to relate the central L-value to an automorphic period integral.  There is a `trivial' bound for this integral, which turns out to correspond to the convexity bound for...

The goal of this talk is to present new results dealing with the asymptotic joint independence properties of commuting strongly mixing transformations along polynomials. These results form natural strongly mixing counterparts to various weakly and...