Micro-conference on C0 topology and related matters

 March 5- 6, 2021.




March 5 ( at the Symplectic Zoominar; for slides and video see the web page:  http://www.math.tau.ac.il/~sarabt/zoominar/ )

Sobhan SeyfaddiniPeriodic Floer homology and  the large-scale geometry of Hofer's metric on the sphere

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.



March 6 (video of the two talks)


9:00 - 10:00  (Montreal time)

Rémi Leclercq, C^0 flexigidity of submanifolds  (slides)

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.

10:30 - 11:30 (Montreal time)

Vincent Humilière, C^0 continuity of spectral invariants and applications (slides)

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.




Organizer: Octav Cornea