S'abonner à l'agenda

S'abonner au séminaire

Ajouter cette URL aux abonnements de votre calendrier électronique :
https://irma.math.unistra.fr/cal/floer-homotopy-theory-%28rencontre-anr-cosy%29-1916.ics
Fermer

Floer Homotopy Theory (Rencontre ANR COSY)


Du 23 au 25 janvier 2024

Salle de conférences IRMA
Programme

La conférence Floer Homotopy Theory aura lieu à l'IRMA du 23 au 25 janvier 2024.

Le but de cette rencontre est de cartographier le domaine émergent de la théorie de l’homotopie de Floer.

Organisateurs : Jean-François Barraud (Toulouse), Mihai Damian (Strasbourg), Vincent Humilière (Paris) et Alexandru Oancea (Strasbourg)

Lieu : salle de conférences de l'IRMA

  • Mardi 23 janvier 2024

  • 08:30

    Accueil
  • 08:45

    Alexandru Oancea, IRMA

    Introduction

  • 09:15

    Simon Allais, IRMA

    Bordism 1 (Bordism groups and Eilenberg-Steenrod axioms)

  • 10:00

    Coffee break
  • 10:30

    Jean-Philippe Chassé, ETH Zurich

    Bordism 2 (Bordism spectral sequence)

  • 11:15

    Break
  • 11:30

    Amanda Hirschi, Sorbonne Université

    Flow categories I (Definitions and examples)

    I will introduce the notion of a flow category and illustrate the definition by explaining how one can associate a flow category to a Morse function. Following Cohen-Jones-Segal, I will sketch how to obtain a CW complex from of a flow category.
  • 12:15

    Lunch Break
  • 14:15

    Colin Fourel, IRMA

    Flow categories 2 (Flow modules and flow bordism groups)

  • 15:00

    Coffee break
  • 15:30

    Mohammed Abouzaid, Stanford

    The Hamiltonian Floer homotopy type I

    I will present the ingredients in the construction of the Floer homotopy type associated to a Hamiltonian diffeomorphism in the language of flow modules, as well as its invariance, following the forthcoming joint paper with A. Blumberg. My goal will be to point out what the technical issues are, and indicate how they are resolved. I will discuss only the symplectically aspherical case in the first lecture.
  • 16:30

    Break
  • 17:00

    Discussion

  • Mercredi 24 janvier 2024

  • 09:00

    Sylvain Courte, Université Grenoble Alpes

    Bordism 3 (Homotopy interpretation of bordism groups I)

  • 09:45

    Coffee break
  • 10:15

    Baptiste Chantraine, Université de Nantes

    Bordism 4 (Homotopy interpretation of bordism groups II)

  • 11:00

    Break
  • 11:15

    Noah Porcelli, Imperial College

    Flow categories 3 (Morse flow bordism groups)

  • 12:00

    Lunch break
  • 14:00

    Mohammed Abouzaid, Stanford

    The Hamiltonian Floer homotopy type II

    The specific topic of the second lecture will be decided based on feedback and interest of the participants.
  • 15:00

    Coffee break
  • 15:30

    Vincent Humilière, Sorbonne Université

    The Eilenberg-MacLane spectrum

  • 16:30

    Break
  • 17:00

    Discussion

  • Jeudi 25 janvier 2024

  • 08:45

    Jean-François Barraud, Université Toulouse III - Paul Sabatier

    Morse homology with DG coefficients

    This is a joint work with M. Damian, V. Humilière, and A. Oancea. I will explain how the usual construction of Morse homology can be enriched to use a DG-local system of coefficients. The main source of examples of such coefficients is given by Hurewicz fibrations on the manifold under consideration, and the construction yields to a Morse theoretic interpretation of the homology (and more precisely of the Leray Serre spectral sequence) of such fibrations. In particular, the invariants retrieved by this construction catch informations that go far beyond the usual homology, and sit midway between homology and homotopy.
  • 09:45

    Coffee break
  • 10:15

    Salammbo Connolly / Frédéric Bourgeois, Université Paris-Saclay

    Floer fundamental groups for Legendrian submanifolds

    We announce two ongoing projects that are based on the Floer fundamental groups introduced by Jean-François Barraud. First, we associate such a group to a generating family describing a Legendrian submanifold, and predict its topological interpretation as a fundamental group. Second, we extend the Barraud construction to obtain representations of Floer fundamental groups, in particular using holomorphic curves for Legendrian submanifolds. These projects are respectively under the co-supervision of and in collaboration with Agnès Gadbled.
  • 11:15

    Pause
  • 11:30

    Paolo Ghiggini, CNRS/Université Grenoble Alpes

    A framed flow category for Khovanov homology

  • 12:30

    Lunch break
  • 12:30

    Repas
  • 14:30

    Noah Porcelli, Imperial College

    Floer theory and cobordism classes of exact Lagrangians

    We apply recent ideas in Floer homotopy theory to some questions in symplectic topology. We show that Floer homology can detect smooth structures of certain Lagrangians, as well as using this to find restrictions on symplectic mapping class groups. This is based on joint work-in-progress with Ivan Smith.
  • 15:30

    Coffee break
  • 16:00

    Discussion