Video Lectures

I will describe constructions of lattice field theories that assign a single bosonic variable to each site, rather a conjugate pair x,p. The information to realize a non-trivial dynamics is realized by non-trivial Poisson brackets between nearest...

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...

The Miura transformation is a powerful formalism to construct generators of vertex operator algebras in free field representation. In this talk, I will explain that Miura operators are R-matrices of a certain quantum algebra, and comment on physical...

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...