Thomas Massoni, of Stanford University, presents joint work with Jonathan Bowden on the symplectic geometry hidden inside dynamical systems. The starting point is a classical construction, due to Mitsumatsu and later generalized by Hozoori, that attaches a Liouville structure on the thickened space [-1,1] x M to any oriented Anosov flow on a closed 3-manifold M. Massoni asks what happens to this structure when two Anosov flows are only orbit equivalent, a much weaker, typically non-smooth relation than conjugacy. He shows that orbit equivalent flows still produce exact symplectomorphic Liouville structures, with an analogous result for taut foliations. The consequence is that symplectic invariants such as Floer homology and the Fukaya category attached to an Anosov flow turn out to be rigid, surviving even this coarse equivalence. Delivered as part of the Joint IAS/PU Symplectic Geometry Seminar at the Institute for Advanced Study, the talk assumes graduate-level familiarity with symplectic topology and dynamical systems.