Thibault Lefeuvre (Université de Paris and Sorbonne Université)

Wednesday, February 21, 2024 - 4:00pm to 5:00pm

PDL C-38

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.

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.