Video Lectures

Fibered 3-manifolds are those constructed via surface homeomorphisms. Given such a manifold with pseudo-Anosov monodromy, much is already known about how topological data of the mapping class determine geometric information about the hyperbolic 3...

In the early 80s Hatcher proved the Smale Conjecture, asserting that the diffeomorphism group of the three-sphere retracts onto its isometry group.  The corresponding problem for RP^3 was open nearly 40 years, and resolved only in 2019 by a detailed...

This talk is based on joint work with Yang Li. I will discuss the problem of counting special Lagrangians in Calabi-Yau 3-folds and Fueter sections to define new numerical and Floer-theoretic invariants. The key challenges are the non-compactness...

High dimensional expansion comes in two flavors: spectral, which relates to random walks;  and cosystolic, which relates to chains of linear maps. The later is a more mysterious notion, which turns out related to a variety of applications such as...

Persistence modules and their associated barcodes were intensively studied since the early 2000s with a view towards applied mathematics. Recently they have also found numerous applications in pure mathematics. We will discuss a few examples from...

Deep generative models offer powerful tools for solving astrophysical inference problems by enabling flexible representations of prior knowledge and likelihood functions.

In the first part of the talk, I will discuss how generative models can be...

Given a triple (X,π,s) consisting of a homogeneous space X=G/P, a dominant weight π giving a projective embedding of X, and a reduced expression s for the minimal coset representative of w_0 in the parabolic quotient W/W_P, we construct a polytope...

It is a classical fact that countable groups of homeomorphisms of the interval and the circle are characterized by purely algebraic properties, namely linear and circular orderability. It remains a difficult and deep problem to understand countable...

I will present recent work with Hairer, Rosati and Yi establishing quantitative lower bounds for the top Lyapunov exponent of linear PDEs driven by two-dimensional stochastic Navier-Stokes equations on the torus. For both the advection-diffusion...

In this talk, we will present a proof of contact big fiber theorem, based on invariants read off from contact Hamiltonian Floer homology. The theorem concludes that any contact involutive map on a Liouville fillable contact manifold admits at least...