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