Workshop on Recent Developments in Symplectic Dynamics

Helicity is an invariant of smooth volume-preserving vector fields on a 3-manifold. Arnold asked whether helicity admits an extension to 𝐶0 volume-preserving flows. In previous work, we constructed such an extension for a large class of 𝐶0 flows.

In...

The ECH "U-map" produces many pseudo-holomorphic curves, but in applications it is sometimes important to have some control on the topology of these curves.  I want to explain how we know that, at least in the case of rational homology spheres,...

We show that on every closed 3-manifold, the pair of oppositely oriented contact structures associated with an Anosov flow completely determines the free homotopy data of its periodic orbits.

As a consequence, using works of Barthlemé-Frankel-Mann...

The structure and growth of various types of Floer homology persistence modules are intimately connected to the dynamics of the underlying Hamiltonian system. For instance, systems with exponential barcode growth have positive topological and metric...

Viterbo’s conjecture predicted that the ball optimizes the systolic ratio among convex domains in 𝑅2𝑛. Motivated by the recent counterexample by Haim-Kislev and Ostrover, and by the connection to Mahler conjecture, one can ask how much symmetry is...