Special year - math workshop

Sponsored by Dr. John P. Hempel 

Organizers: Marie-Claude Arnaud, Michael Hutchings, Tere Seara, Alfonso Sorrentino, and Claude Viterbo

This workshop will focus on recent developments in symplectic, Hamiltonian, and contact dynamics. There will be an...

Viterbo’s conjecture predicted that the ball optimizes the systolic ratio among convex domains in $R^{2n}$. Motivated by the recent counterexample by Haim-Kislev and Ostrover, and by the connection to Mahler conjecture, one can ask how much symmetry...

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...

I will report on some joint work in progress with Lev Buhovsky and Sobhan Seyfaddini, where we study whether the spectral invariants of Hamiltonian homeomorphisms of surfaces are "spectral", i.e. correspond to the action of fixed points. This...

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...

Helicity is an invariant of smooth volume-preserving vector fields on a 3-manifold. Arnold asked whether helicity admits an extension to $C^0$ volume-preserving flows. In previous work, we constructed such an extension for a large class of $C^0$...

Helicity is an invariant of smooth volume-preserving vector fields on a 3-manifold. Arnold asked whether helicity admits an extension to $C^0$ volume-preserving flows. In previous work, we constructed such an extension for a large class of $C^0$...

We will discuss some recent results around the stability theory of elliptic equilibria of real analytic Hamiltonian flows. 
 

In this talk, we discuss a new approach to the Hofer-Zehnder conjecture for non-degenerate dynamically convex Reeb flows, along with some results obtained from this perspective. The talk is based on joint work in progress with Erman Cineli and...