Previous Conferences & Workshops

The method of hypergraph containers is a widely-applicable technique in probabilistic combinatorics. The method enables one to gain control over the independent sets of many `interesting' hypergraphs by exploiting the fact that these sets exhibit a...

Given a quasi projective family S of complex algebraic varieties, its Hodge locus is the locus of points of S where the corresponding variety admits exceptional Hodge classes (conjecturally: exceptional algebraic cycles). In this talk, I will survey...

Structures which minimise area appear in numerous geometric contexts often related to degeneration phenomena. In turn, in many situations these structures also reflect the ambient geometry in some way (they are ‘calibrated’) and so they may provide...

About 20 years ago, Gurvits developed the notion of polynomial capacity to give a simple proof of the famous van der Waerden lower bound on the permanent of a doubly stochastic matrix. Since then, similar techniques have led to various other...

We will discuss a graph that encodes the divisibility properties of integers by primes. We will prove that this graph has a strong local expander property almost everywhere. We then obtain several consequences in number theory, beyond the...

Prove that for a qcqs analytic adic space $X$, the category of nuclear sheaves on $X$ is dualizable in two steps. First, establish the result locally over affinoid Tate adic spaces using the notion of weak proregularity and then prove a general...

Let $G$ be a compact Lie group acting on a closed manifold $M$. Partially motivated by work of Uhlenbeck (1976), we explore the generic properties of Laplace eigenfunctions associated to $G$-invariant metrics on $M$. We find that, in the case where...

I will introduce Apollonian circle packings, and describe the local-global conjecture, which predicts the set of curvatures of circles occurring in a packing. I will then describe reciprocity obstructions, a phenomenon rooted in reciprocity laws...