Video Lectures

In 1962, Yudovich established the well-posedness of the two-dimensional incompressible Euler equations for solutions with bounded vorticity. However, uniqueness within the broader class of solutions with L^p vorticity remains a key unresolved...

Although current large language models are complex, the most basic specifications of the underlying language generation problem itself are simple to state: given a finite set of training samples from an unknown language, produce valid new strings...

In this talk, we will explore the relationship between the geometry and topology of a complexity-one four-manifold and the combinatorial data that encode it. We will use a generators-and-relations description for the even part of the equivariant...

Configuration spaces of points in graphs are nonsmooth analogs of braid arrangements, appearing in robotics applications and in theory of moduli spaces of tropical curves. While their cohomology is extremely difficult to understand, and depends on...

In this talk I will explain some quantitative embedding results for Legendrian submanifolds of pre-quantization spaces. To start, I will recall some contact non-squeezing results for domains, and present an elementary proof of Legendrian non...

We define the systolic $S^1$-index of a convex body as the Fadell–Rabinowitz index of the space of centralized generalized systoles associated with its boundary. We show that this index is a symplectic invariant. Using the systolic $S^1$-index, we...

Given a finite collection of disjoint Lagrangian circles on a symplectic surface satisfying some area constraints, Cristofaro-Gardiner, Humilière, Mak, Seyfaddini and Smith define a link spectral invariant, by computing the Lagrangian Floer homology...

In algebraic geometry, the Ceresa cycle provided one of the first examples of a nullhomologous cycle which is not algebraically trivial. I will explain how one can obtain a mirror statement about the Lagrangian Ceresa cycle, a nullhomologous...