Previous Conferences & Workshops

Let $X$ be a K3 surface. Consider a finitely supported probability measure $\mu$ on $\operatorname{Aut}(X)$ such that $\Gamma_{\mu} = \langle \operatorname{Supp}(\mu)\rangle Aut(X)$ is non-elementary. We do not assume that $\Gamma_{\mu}$ contains...

Around 1992, Aldous made the following bold conjecture. Let A be any set of transpositions in the symmetric group Sym(N). Then the spectral gap of the Cayley graph Cay(Sym(N),A) is identical to that of a relatively tiny N-vertex graph defined by A...

The Shafarevich conjecture is concerned with finiteness results for families of g-dimensional principally polarized abelian varieties over a base B. Famously, Faltings settled the arithmetic case of B=O_{K,S}. In the case where B is a curve over a...

I'll give a brief introduction to o-minimality and how it can be used to prove asymptotic estimates for the number of rational points in definable sets. I'll then show how problems from various areas of mathematics can be reformulated as questions...

In this talk, I will describe our construction of the first explicit lossless vertex expanders. These are graphs where every small subset of vertices has about as many neighbors as their sparsity allows. Previously, the strongest known explicit...

In characteristic zero, Castelnuovo proved that every unirational surface is rational. In positive characteristic, this fails dramatically: there exist many non-rational, often even general-type, surfaces that are nevertheless unirational. In 1977...

I will describe recent work in progress on logarithmic--exponential preparation theorems in analytically generated sharply o-minimal structures. Our results imply the sharp o-minimality of $\mathbb{R}_{\exp}$ as well as a uniform version of Wilkie’s...

Property (T) was defined by Kazhdan in the 1960s, who used it to prove two conjectures of Selberg on lattices in high-rank Lie groups. Shortly after that, Margulis used it to construct expander graphs.

Property $\tau$ is a baby version of property (T...