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
- 10h30-11h : Accueil en salle cafete
- 11h-12h : Russell Avdek (exposé 1)
- Déjeuner à l'oiseau blanc
- 13h30-14h30 : Paolo Ghiggini
- 15h-16h : Russell Avdek (exposé 2)
- pause
- 16h30-17h30 : Marco Mazzucchelli
- Dîner à Grenoble (restaurant à déterminer)
Vendredi 1 décembre
- 10h30-11h30 : Laura Marino (séminaire de topologie)
- Déjeuner à l'oiseau blanc
- 13h30-14h30 : Russell Avdek (exposé 3)
- pause
- 15h-16h30 : Discussions
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.