Previous Conferences & Workshops

A meandric system of size $n$ is the set of loops formed from two arc diagrams (non-crossing perfect matchings) on $\{1,\dots,2n\}$, one drawn above the real line and the other below the real line. Equivalently, a meandric system is a coupled...

Abstract: A subset of a group is said to be product free if it does not contain the product of two elements in it. We consider how large can a product free subset of the alternating group $A_n$ be? 

In the talk we will completely solve the problem...

Abstract: Approximate lattices in locally compact groups are approximate subgroups that are discrete and have finite co-volume. They provide natural examples of objects at the intersection of algebraic groups, ergodic theory and additive...

Abstract: Work of Mark Shusterman and myself has proven an analogue of Chowla's conjecture for polynomial rings over finite fields, which controls k-points correlations of the Möbius function for k bounded by a certain function of the finite field...

The linearization method of Dani-Margulis controls the amount of time a unipotent trajectory spends near invariant subvarieties of a homogeneous space. I will describe a problem in number theory where a similar control is desired for diagonalizable...

Abstract: We present recent work, joint with J. Wolf, in which we define a natural ternary analogue of the order property, called the functional order properly, and show that subsets of $F_p^n$ without the functional order property admit especially...

Abstract: In this talk, I will discuss a proof of a quantitative version of the inverse theorem for Gowers uniformity norms $\mathsf{U}^5$ and $\mathsf{U}^6$ in $\mathbb{F}_2^n$. The proof starts from an earlier partial result of Gowers and myself...

Abstract: I will discuss the difficult problem of proving reasonable bounds in the multidimensional generalization of Szemer\’edi’s theorem and describe a proof of such bounds for sets lacking nontrivial configurations of the form $(x,y), (x,y+z),...

I've been working a lot on "random surfaces" in recent years.  These are "canonical" random fractal Riemannian manifolds (just as Brownian motion is a canonical random fractal curve) and they come up in many areas of physics and mathematics.  In a...