Nantes Université - Université Paris-Saclay

NANTES-ORSAY SEMINAR ON
SYMPLECTIC AND CONTACT GEOMETRY

Friday, 22 November 2024

Rémi Leclercq (Orsay)

Topological properties of orbits of Lagrangians and the Lagrangian C⁰ Flux conjecture

Abstract: In this talk, based on a joint work with Jean-Philippe Chassé, I will explain conditions under which a Lagrangian L admits a "Weinstein neighborhood of Hamiltonian (resp. symplectic) non-displacement", i.e. a neighborhood W such that any Lagrangian in the Hamiltonian (resp. symplectic) orbit of L, included in W, must intersect L. This result follows from exactness of nearby Lagrangians: any Lagrangian in the orbit of L, included in W, is exact in W seen as a subset of the cotangent bundle of L. Moreover, I will discuss several applications, in particular to the Lagrangian C⁰ flux conjecture and to the topology of orbits of Lagrangians.

Joé Brendel (Zurich)

Classification of split tori in S² × S² and applications

Abstract: A split torus in S² × S² is a Lagrangian torus obtained as the product of circles in the factors. The goal of this talk is to give a classification up to symplectomorphisms of such tori and illustrate that interesting things happen in case the symplectic form is non-monotone. Among other applications, we will answer a question about Lagrangian packings posed by Polterovich-Shelukhin. This is partially based on joint work with Joontae Kim.

Informal discussions