Differential geometry and symplectic topology seminar (Fall 2025)

Abstracts

• Julian Chaidez

  • Pseudo-Anosov flows, originally introduced by Thurston, are a broad class of hyperbolic flows on 3-manifolds that are Anosov except along a finite link of singular closed orbits. A longstanding conjecture states that any 3-manifold carries only finitely many transitive pseudo-Anosov flows, up to the appropriate type of equivalence. In this talk, I will explain a proof of this conjecture for a large class of pseudo-Anosov flows that are Reeb, in the appropriate sense. This extends recent work by Barthelme-Bowedn-Mann for Reeb Anosov flows. The proof involves a computation of cylindrical contact homology in this setting. This is joint work in preparation with Yijie Pan (USC).

• Peter Olver

  • I will present a new theorem proving convergence of normal form series for a broad range of Lie pseudo-group actions on submanifolds. This result generalizes the normal forms of Chern and Moser for hypersurfaces in CR geometry. The proof relies on combining the theory of involutive systems of partial differential equations with the method of equivariant moving frames. Joint work with Francis Valiquette and Masoud Sabzevari.