Video Lectures

Fekete (1923) discovered the notion of transfinite diameter while studying the possible configurations of Galois orbits of algebraic integers in the complex plane. Based purely on the fact that the discriminants of monic integer irreducible...

Langevin diffusions are continuous-time stochastic processes that are based on the gradient of a potential function. As such they have many connections---some known and many still to be explored---to gradient-based machine learning. I'll discuss...

The IAS Number Theory group has started a new online seminar via Zoom to have more interactions among members during the Stay-at-Home Order. The seminar is modeled after the Basic Notions seminar at Harvard and is intended to be a one-hour-long Math...

Large-scale vision benchmarks have driven---and often even defined---progress in machine learning. However, these benchmarks are merely proxies for the real-world tasks we actually care about. How well do our benchmarks capture such tasks? In this...

A transverse link in a contact 3-manifold forces topological entropy if every Reeb flow possessing this link as a set of periodic orbits has positive topological entropy. We will explain how cylindrical contact homology on the complement of...

In this talk we will be addressing the question whether a given Lagrangian torus in a toric monotone symplectic manifold can be realized as the fixed point set of an anti-symplectic involution (in which case it is called "real"). In the case of...

Gromov nonsqueezing tells us that symplectic embeddings are governed by more complex obstructions than volume. In particular, in 2012, McDuff-Schlenk computed the embedding capacity function of the ball, whose value at a is the size of the smallest...

One of the fundamental challenges in number theory is to understand the intricate way in which the additive and multiplicative structures in the integers intertwine. We will explore a dynamical approach to this topic. After introducing a new...

Wave maps are harmonic maps from a Lorentzian domain to a Riemannian target. Like solutions to many energy critical PDE, wave maps can develop singularities where the energy concentrates on arbitrary small scales but the norm stays bounded. Zooming...

I will explain a duality theorem with products in Rabinowitz-Floer homology. This has a bearing on string topology and explains a number of dualities that have been observed in that setting. Joint work in progress with Kai Cieliebak and Nancy...