Video Lectures

A few years ago, Bhatt-Morrow-Scholze introduced an invariant of p-adic formal schemes called syntomic cohomology, which has a close relationship to (étale-localized) algebraic K-theory. In a recent paper, Antieau-Mathew-Morrow-Nikolaus showed that...

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...

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...

Since the beginning of the subject, it has been speculated that Gromov-Witten invariants should admit refinements in complex cobordism. I will propose a resolution of this question based on joint work-in-progress with Abouzaid, building on recent...

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...

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 𝕋 is a...

I will discuss escape of mass estimates for SL(d,ℝ)-horospheres embedded in the space of affine lattices, which depend on the Diophantine properties of the shortest affine lattice vector. These estimates can be used, in conjunction with Ratner's...

In this talk, I will present a computation of the image of the Hodge-Tate logarithm map (defined by Heuer) in the case of smooth Stein varieties. When the variety is the affine space, Heuer has proved that this image is equal to the group of closed...

Agreement testing (aka direct product testing), checks if consistent local information reveals global structure. Beyond its theoretical connections to probabilistic checkable proofs (PCPs), constructing agreement testers is a fundamental...