Video Lectures

The notion of singular support has its origin in the theory of partial differential equations, and was introduced to the world of constructible sheaves by M. Kashiwara and P. Schapira in the 1970s. It is a basic invariant (like the support), and...

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...

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...