researchseminars.org

Sobhan Seyfaddini (at the Symplectic Zoominar)
2021-03-05 14:15 - 15:15 UTC | https://stable.researchseminars.org/talk/Micro-C0-conf/1/
Title: Periodic Floer homology and the large-scale geometry of Hofer's metric on the sphere (https://stable.researchseminars.org/talk/Micro-C0-conf/1/)
by Sobhan Seyfaddini (at the Symplectic Zoominar) as part of Micro-Conference on C0 symplectic topology

Abstract
The group of Hamiltonian diffeomorphisms of a symplectic manifold admits a remarkable bi-invariant metric, called Hofer’s metric. My talk will be about a recent joint work with Dan Cristofaro-Gardiner and Vincent Humilière resolving the following two open-questions related to the large-scale geometry of this metric. The first, due to Kapovich and Polterovich, asks whether the two-sphere, equipped with Hofer’s metric, is quasi-isometric to the real line; we show that it is not. The second, due to Fathi, asks whether the group of area and orientation preserving homeomorphisms of the two-sphere is a simple group; we show that it is not. Key to our proofs is a new sequence of spectral invariants defined via Hutchings’ Periodic Floer Homology.

Rémi Leclercq
2021-03-06 14:00 - 15:00 | https://stable.researchseminars.org/talk/Micro-C0-conf/2/
Title: C^0 flexigidity of submanifolds (https://stable.researchseminars.org/talk/Micro-C0-conf/2/)
by Rémi Leclercq as part of Micro-Conference on C0 symplectic topology

Abstract
We will review recent results in C^0 symplectic geometry. In this first part we will be interested in problems of rigidity and flexibility of some natural submanifolds of symplectic manifolds. We will focus on rigidity results for coisotropic submanifolds, obtained in joint works with Humilière and Seyfaddini.

Vincent Humilière
2021-03-06 15:30 - 16:30 | https://stable.researchseminars.org/talk/Micro-C0-conf/3/
Title: C^0 continuity of spectral invariants and applications (https://stable.researchseminars.org/talk/Micro-C0-conf/3/)
by Vincent Humilière as part of Micro-Conference on C0 symplectic topology

Abstract
In this second part on C^0 symplectic geometry, we will review recent results on the C^0 continuity of spectral invariants (and barecodes), in particular those obtained in joint work with Lev Buhovsky and Sobhan Seyfaddini. We will also present various consequences and applications of this continuity.
