Video Lectures

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...

This talk will report on an REU whose goal was to introduce the notion of persistence into Legendrian contact homology. The LCH of a Legendrian knot is computed as the homology of the knot's Chekanov-Eliashberg DGA and is a well-studied invariant of...

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...

The cosmic history of galaxy formation is the history of star formation writ large.  Some of the most important processes affecting galaxy evolution involve coupling between stellar and gaseous components, since massive stars are the primary energy...

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...

Will future large-scale water resources plans make compelling arguments for including the reduction of the loss of biodiversity across scales in fluvial landscapes? Is the structure of river networks a template for the large-scale spread of...

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...