Rencontre ANR COSY Lyon-Grenoble autour de la géométrie symplectique et de contact

30 novembre et 1 décembre 2023, Institut Fourier, Grenoble

(rez-de-chaussée, salle de lecture B29)

Jeudi 30 novembre

Vendredi 1 décembre

Titre et résumé des exposés

  • Russell Avdek (mini-cours) : Contact submanifolds and their stabilizations in high dimensions

    This mini-course concerns generalizing some concepts from low-dimensional contact topology to higher dimensions. After reviewing some foundations and important examples, we'll describe a stabilization operation for codim=2 contact submanifolds in high dimensions using handle attachment surgeries. Our goal will then be to prove that a contact manifold of dimension at least 5 is overtwisted iff its ``standard contact unknot'' is stabilized.

  • Paolo Ghiggini : A relative exact sequence for Lagrangian Floer homology.

    Some years ago Chantraine, Dimitroglou-Rizell, Golovko and I defined a version of Lagrangian Floer homology for Lagrangian cobordisms also known as Cthulhu homology. I will show that concatenation of cobordisms induce a long exact sequence in Cthulhu homology. A similar exact sequence was proved by Cieliebak and Oancea if the negative ends of the cobordisms are filled.

  • Marco Mazzucchelli : Locally maximal closed orbits of Reeb flows

    A compact invariant set of a flow is called locally maximal when it is the largest invariant set in some neighborhood. In this talk, based on joint work with Erman Cineli, Viktor Ginzburg, and Basak Gurel, I will present a "forced existence" result for the closed orbits of certain Reeb flows on spheres of arbitrary odd dimension: - If the contact form is non-degenerate and dynamically convex, the presence of a locally maximal closed orbit implies the existence of infinitely many closed orbits. - If the locally maximal closed orbit is hyperbolic, the assertion of the previous point also holds without the non-degeneracy and with a milder dynamically convexity assumption. These statements extend to the Reeb setting earlier results of Le Calvez-Yoccoz for surface diffeomorphisms, and of Ginzburg-Gurel for Hamiltonian diffeomorphisms of certain closed symplectic manifolds.