Previous Conferences & Workshops

In 1975, Szemer\'edi proved that any subset of the natural numbers with positive upper density must contain arbitrarily long finite arithmetic progressions. Szemer\'edi's original argument was purely combinatorial, and then Furstenberg gave an...

In 2023, Raghu Meka and I proved a substantially improved bound on the size of the smallest set of integers in [N] which contains no 3-term arithmetic progression. Since then, it has become clear that the main new ideas from that work are in fact...

We will discuss an inductive approach to determining the asymptotic number of G-extensions of a number field with bounded discriminant, and outline the proof of Malle's conjecture in numerous new cases. This talk will include discussions of several...

A valuation is a finitely additive measure on the class of all convex compact subsets of $R^n$. Over the past two decades, a number of structures has been discovered on the space of translation invariant smooth valuations. Recently, these findings...

In primary school, I never got beyond adding integers and the questions have only been piling up since! What do sets of integers $A$ look like if they generate only a few sums with the elements of another set $B$? Meester Jaap (my primary teacher)...

Influential work of Hodge from the 1940s led the way in using Gröbner bases to combinatorially study the Grassmannian. We follow Hodge's approach to investigate certain subvarieties of the Grassmannian, called positroid varieties. Positroid...

 We prove ''reasonable'' quantitative bounds for sets in $\mathbb{Z}^2$ avoiding the ${polynomial}$ ${corner}$ ${configuration}$ $(x,y), (x+P(z),y), (x,y+P(z))$, where $P$ is any fixed integer-coefficient polynomial with an integer root of...

In this overview talk we will explore a variational approach to the problem of Spectral Minimal Partitions (SMPs).  The problem is to partition a domain or a manifold into k subdomains so that the first Dirichlet eigenvalue on each subdomain is as...