Séminaires : Phd Seminar - Séminaire des doctorant.e.s

Le séminaire des doctorant.e.s est l'occasion pour les doctorant.e.s de présenter des résultats et des problématiques dignes d'intérêt devant un public de non-spécialistes. L'ambiance y est informelle ; poser des questions naïves est encouragé, et les questions moins naïves sont bienvenues dans la mesure où elles n'entravent pas le bon déroulement de l'exposé.

Chaque jeudi à 18h, en alternance entre Jussieu et Sophie Germain.

The PhD seminar is an opportnuity for PhD students to present results and topics worthy of interest in front of a non-specialist audience. The mood is informal ; asking naive questions is highly encouraged and less naive questions are also welcomed, as long as they don't intefere with the smoothness of the talk.

Every Thursday at 6pm, alternating between Jussieu and Sophie Germain.

Exact Lagrangian submanifolds and Hamiltonian diffeomorphisms play a central role in symplectic topology, particularly in problems related to Arnold’s conjecture on fixed points and Lagrangian intersections. Using Floer theory, one can associate spectral invariants to these objects that lead to a metric on the sets of exact Lagrangian submanifolds and Hamiltonian diffeomorphisms and also to the question of understanding the limit under this metric. This motivates the study of completion of these sets that were firstly studied by Vincent Humilière, as well as the notion of γ-support associated to elements of these completions that has recently been developed by Claude Viterbo. In this talk, after reviewing some preliminaries in symplectic topology, I will introduce the notion of γ-support, describe some of its properties, and discuss its applications. If time permits, I will also briefly discuss my ongoing thesis work on a notion of density for the γ-support and its relation to the regularity of the γ-support in a neighborhood of a point.

[V22] Claude Viterbo, On the Supports in the Humilière Completion and γ - Coisotropic Sets. To appear in Journal de l'École polytechnique

[AHV24] Marie-Claude Arnaud, Vincent Humilière, and Claude Viterbo, Higher Dimensional Birkhoff Attractors. To appear in Journal de L'École Polytechnique

[H08] Vincent Humilière, On Some Completions of the Space of Hamiltonian Maps. Bulletin de la Soc. Math. de France 136.3, PP. 373–404 (2008).