EVENT DETAILS AND ABSTRACT

Title: Isospectral connections, frame flow ergodicity, and polynomial maps between spheres
Speaker: Thibault Lefeuvre
Speaker Info: Sorbonne University
Brief Description:
Special Note:
Abstract:

Classifying real polynomial maps between spheres is a challenging problem in real algebraic geometry. Remarkably, this question has found recent applications in two seemingly unrelated fields: - in spectral theory, it allowed to solve Kac's celebrated isospectral problem (Can one hear the shape of a drum?) for the connection Laplacian. - in dynamical systems, it allowed to prove ergodicity for a certain class of partially hyperbolic flows (extensions of the geodesic flow on negatively-curved manifolds). I will explain these problems and how they all connect together. No prerequisite required -- the talk is intended for a broad audience. Joint work with Mihajlo Cekić.