02/01: Kurt Vinhage

Entropy Rigidity for Anosov Flows in Dimension Three

Abstract: In the 80’s, A. Katok proved that for a geodesic flow on a negatively curved surface, coincidence of its entropy with respect to the Liouville measure with its topological entropy is equivalent to that surface being hyperbolic. The Katok Entropy conjecture states that similar conclusions should hold in higher dimensions as well. In this talk, I will discuss recent work, joint with Jacopo de Simoi, Martin Leguil and Yun Yang, which extends the scope of the rigidity phenomenon to Anosov flows in three dimensions. Time permitting, I will discuss ongoing progress in the dual question of entropy flexibility