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

https://us02web.zoom.us/j/86751202563?pwd=ZHNKM2c1WllnS1VHakFOeDNVaWRtUT09

**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)