IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar
9:15am|Remote Access
Topic: Regularity and Persistence in Non-Weinstein Liouville Geometry via Hyperbolic Dynamics
Speaker: Surena Hozoori
Affiliation: University of Rochester
Date: January 24, 2025
We explore the construction of non-Weinstein Liouville geometric objects based on Anosov 3-flows, introduced by Mitsumatsu, in the generalized framework of Liouville Interpolation Systems and non-singular partially hyperbolic flows. We discuss the subtle phenomena inherited from the regularity and persistence theory of hyperbolic dynamics in the resulting Liouville structures, and prove dynamical and geometric rigidity results in this context. Among other things, we show that Mitsumatsu's examples characterize 4-dimensional non-Weinstein Liouville geometry with 3-dimensional C1
-persistent transverse skeleton. Time permitting, we also draw applications to the regularity theory of the weak dominated bundles for non-singular partially hyperbolic 3-flows.