Seminars Sorted by Series

Abstract: Several equivalent definitions of rank for matrices yield non-equivalent definitions of rank when generalized to higher order tensors. Understanding the interplay between these different definitions is related to important questions in...

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...

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 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: 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: 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...

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),...

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: 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: 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...

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: 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...

Combinatorics of Enumerative Geometry

Organizers: Paolo Aluffi, Dave Anderson, June Huh, and Leonardo Mihalcea

This workshop is dedicated to the exploration of the combinatorial dimensions of intersection theory and enumerative geometry, broadly...