Lieu: IHP, salle 201 le matin et amphi Darboux l'après-midi
The seminar will take place in presence, but will be broadcasted via zoom
10:45 Anna Florio (Dauphine)
Right-handed flows on $S^3$ and a quantitative condition to find explicit examples.
Abstract: Global surfaces of section for Reeb flows in dimension 3 are powerful tools to study the associated dynamics. Among Reeb flows on the 3-sphere, those that are right-handed in the sense of Ghys exhibit lots of such global surfaces of section: indeed, Ghys proved that for a right-handed flow any finite (non-empty) collection of periodic orbits is the boundary of a global surface of section. In a joint work with U. L. Hryniewicz, we give a sufficient condition to assure that a flow is right-handed. After presenting our condition, we discuss applications, notably to strictly convex energy levels of Hamiltonian flows on $\R^4$ and to Riemannian geodesic flows on the 2-sphere.
14:00 Cheuk-Yu Mak (Edimbourgh)
Quasimorphisms and Lagrangian links on the 2-sphere
Abstract: When a group G is simple, there is no non-trivial homomorphism from G to the real line but G can possibly have a lot of quasimorphisms. It makes quasimorphisms an important concept in studying groups. In particular, it is an interesting question to ask how many quasimorphisms a group has. In this talk, I will explain how to use Floer theory to construct uncountably many linearly independent homogeneous quasimorphisms on the area-preserving diffeomorphism/homeomorphism group of the 2-sphere, which answers a question of Entov-Polterovich-Py. This is based on a joint work with Daniel Cristofaro-Gardiner, Vincent Humilière, Sobhan Seyfaddini and Ivan Smith.
15:45 HDR defense of Maxime Zavidovique (Jussieu)
Discrete Weak KAM Theory: an introduction through examples and its applications to twist maps.
Prochaines séances: 7 janvier (A. Keating, E. Cineli, ?), 4 février (M.
Bertelson, ?, ?)
Autre activité symplectique à Paris:
- Séminaire Nantes-Orsay (à Nantes le 10 décembre)