Previous Conferences & Workshops

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...

Abstract: A theorem by Kazhdan and Ziegler says that any property of homogeneous polynomials---of a fixed degree but in an arbitrary number of variables---that is preserved under linear maps is either satisfied by all polynomials or else implies a...

This is joint work with Haolin Shi (Yale). 3-webs are bipartite, trivalent, planar graphs. They were defined and studied by Kuperberg who showed that they correspond to invariant functions in tensor products of $SL_3$-representations. Webs and...

Abstract: Ellenberg and Gijswijt drastically improved the best known upper asymptotic bound for the cardinality of a cap set in 2016. Tao introduced the notion of slice rank for tensors and showed that the Ellenberg-Gijswijt proof can be nicely...

Abstract: Let V be a complex vector space and consider symmetric d-linear forms on V, i.e., linear maps $Sym^d(V) \rightarrow > C$. When V is finite dimensional and $d>2$, the structure of such forms is very complicated. Somewhat surprisingly, when...

Abstract: The Alon-Jaeger-Tarsi conjecture states that for any finite field $F$ of size at least 4  and any nonsingular  matrix $M$ over $F$ there exists a vector $x$ such that neither $x$ nor $Mx$ has a 0 component. In this talk we discuss the...

Abstract: Let $f:{0,1}^n$ to ${0,1}$ be a boolean function. It can be uniquely represented as a multilinear polynomial. What is the structure of its monomials? This question turns out to be connected to some well-studied problems, such as the log...