Video Lectures

Spatially resolved polarimetric images of black holes with the Event Horizon Telescope (EHT) favor models with strong magnetic fields, so-called Magnetically Arrested Disks or MAD models.  MADs can produce efficient jets via the Blandford-Znajek (BZ...

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...

The Navier–Stokes (NS) equations describe fluid dynamics through a high-dimensional, nonlinear partial differential equations (PDEs) system. Despite their fundamental importance, their behavior in turbulent regimes remains incompletely understood...

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...

For an elliptic curve E defined over Q, the Mordell-Weil group E(Q) is a finitely generated abelian group. We prove that there are infinitely many elliptic curves E over Q for which E(Q) has rank 2. Our elliptic curves will be given by explicit...