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Isospectral connections, frame flow ergodicity, and polynomial maps between spheres

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
- 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.
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