Video Lectures

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...

If f is a real polynomial and A and B are finite sets of cardinality n, then Elekes and Ronyai proved that either f(A×B) is much larger than n, or f has a very specific form (essentially, f(x,y)=x+y). In the talk I will tell about an analogue of...

Given an area-preserving surface diffeomorphism, what can one say about the topological properties of its periodic orbits? In particular, a finite set of periodic orbits gives rise to a braid in the mapping torus, and one can ask which isotopy...

Zeros of L-functions have been extensively studied, due to their close connection to arithmetic problems. Despite several precise conjectures about their behavior, our unconditional understanding of them remains limited. In this talk we will discuss...