## Spectral characterizations of Besse and Zoll Reeb flows

Marco Mazzucchelli

École normale supérieure de Lyon

May 8, 2020

In this talk, I will address a geometric inverse problem from contact geometry: is it possible to recognize whether all orbits of a given Reeb flow are closed from the knowledge of the action spectrum? Borrowing the terminology from Riemannian geometry, Reeb flows all of whose orbits are closed are sometimes called Besse, and Besse Reeb flows all of whose orbits have the same minimal period are sometimes called Zoll.