Speaker
2024 Rolf Schock Prize in Mathematics laurete, Professor Lai-Sang Young, Courant Institute, New York University, New York
Abstract
This talk summarizes developments in dynamical systems from an observational viewpoint, for systems that are deterministic or random, in finite or infinite dimensions. In finite dimensions, observable events are often equated with positive Lebesgue measure sets, and simple examples suggest that Lebesgue measure transported forward converges to either a stable equilibrium or a special invariant measure called an SRB measure. While this picture may be overly simplistic for deterministic systems, it has been shown — under mild assumptions — to be valid under stochastic perturbations. I will
discuss next the idea of observability for infinite dimensional dynamical systems. I will propose a notion that is a natural generalization of ideas in finite dimensions, and explain why with this notion, a number of results may carry over to infinite dimensions, to systems such as semiflows generated by some evolutionary PDEs.