Symplectic Rigidity of Anosov Flows Under Orbit Equivalence

Explore the symplectic rigidity properties of Anosov flows through this advanced mathematics seminar lecture from the Joint IAS/PU Symplectic Geometry Seminar. Delve into the classical Mitsumatsu construction and its generalization by Hozoori, which associates Liouville structures on thickened 3-manifolds to oriented Anosov flows and suitable taut foliations. Examine the fundamental question of how orbit equivalence—homeomorphisms that preserve unparametrized orbits but are typically non-smooth—affects the associated Liouville structures. Discover groundbreaking research demonstrating that orbit equivalent Anosov flows induce exact symplectomorphic Liouville structures, with analogous results extending to taut foliations. Learn how this remarkable rigidity result implies that symplectic invariants including Floer homology and Fukaya categories remain preserved under orbit equivalence, establishing deep connections between dynamical systems and symplectic geometry. Gain insights into cutting-edge techniques at the intersection of geometric topology, dynamical systems, and symplectic geometry through detailed mathematical exposition and proof strategies.