Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

Lukas Nakamura (University of Upsala):

A Metric on the Contactomorphism Group of an Orderable Contact Manifold: We discuss some properties of a pseudo-metric on the contactomorphism group of a strict contact manifold M induced by the maximum/minimum of Hamiltonians. We show that it is non-degenerate if and only if M is orderable and that its metric topology agrees with the interval topology introduced by Chernov and Nemirovski. We also discuss analogous results on isotopy classes of Legendrian submanifolds and on universal covers.

Habib Alizadeh (University of Montreal):

Fragmentation in Dimension Four and its Application to Spectral Estimators: We show a new Hamiltonian fragmentation result for four-dimensional symplectic polydisks. As an application to our result, we prove $C^0$-continuity of the spectral estimators defined by Polterovich and Shelukhin for polydisks.

Han Lou (University of Georgia, Athens):

On the Hofer Zehnder Conjecture for Semipositive Symplectic Manifolds: Arnold conjecture says that the number of 1-periodic orbits of a Hamiltonian diffeomorphism is greater than or equal to the dimension of the Hamiltonian Floer homology. In 1994, Hofer and Zehnder conjectured that there are infinitely many periodic orbits if the equality doesn't hold. In this talk, I will show that the Hofer-Zehnder conjecture is true for semipositive symplectic manifolds with semisimple quantum homology. This is a joint work with Marcelo Atallah.