Previous Conferences & Workshops

In this talk, we will discuss the behavior of the Yamabe flow on an asymptotically flat (AF) manifold. We will first show the long-time existence of the Yamabe flow starting from an AF manifold and discuss the uniform estimates on manifolds with...

Algorithms for understanding data generated from distributions over large discrete domains are of fundamental importance.  In this talk, we consider the sample complexity of *property testing algorithms* that seek to to distinguish whether or not an...

Curve counting invariants such as Gromov-Witten invariants are rational numbers in general because they are essentially certain orbifold Euler characteristics. In 1997 Fukaya-Ono proposed that by using the complex nature of the pseudoholomorphic...

The interchange process \sigma_T is a random permutation valued process on a graph evolving in time by transpositions on its edges at rate 1. On Z^d, when T is small all the cycles of the permutation \sigma_T are finite almost surely. In dimension d...

The Cohen-Lenstra heuristics give predictions for the distribution of the class groups of a random quadratic number field. Cohen and Martinet generalized them to predict the distribution of the class groups of random extensions of a fixed base field...

In these two talks, I will discuss the structure of certain varieties that depend functorially on the choice of a finite-dimensional vector space. Examples include the variety of d-way tensors of "slice rank" at most k and the variety of degree-d...

In 1939, Mahler asked whether the product of the volumes of a centrally symmetric convex body and its polar is minimized by a cube. He gave a positive answer to this question in dimension 2. In this talk I will explain how this is related to...

Lower scalar curvature bounds on spin Riemannian manifolds exhibit remarkable rigidity properties determined by spectral properties of Dirac operators. For instance, a fundamental result of Llarull states that there is no smooth Riemannian metric on...

Given a topological dynamical system $(X,T)$ a bounded sequence $(a_n)$ and $f\in C(X)$ we are interested in the asymptotic behavior of $$\frac{1}{\sum_{n\leq N}|a_n|}\sum_{n\leq N}a_nf(T^nx)$$

This will be a survey talk about recent progress on pointwise convergence problems for multiple ergodic averages along polynomial orbits and their relations with the Furstenberg-Bergelson-Leibman conjecture.