Video Lectures

A sparsification of a structure, with respect to a class of queries, produces a compressed representation of the structure while answering every query in the class approximately correctly. The seminal example of sparsification is "graph...

I will describe a problem of unlikely intersections in a product of modular curves, tracing the problem itself and the tools for some results through the work of Enrico.

Most effective results for integral points on affine curves use the works of Baker or Bombieri on Diophantine approximation by S-units. Still, no completely general result is known already in genus 2. I will briefly present some recent work with...

It has been a continuing interest, often with profound importance, in understanding the geometric and topological relationship between a Hamiltonian G-manifold Y and a symplectic quotient X. In this talk, we shall provide precise relations between...

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...