Program*

31 Jan. 1 Feb. 2 Feb.
9:00-11:00 Accueil,
first discussions...
9:00-10:00 Salamon 9:00-10:00 Polterovich
10:00-10:30Coffee break 10:00-10:30Coffee break
10:30-11:30 Welschinger 10:30-11:30 McLean
12:00-14:00Lunch 12:00-14:00Lunch 12:00-14:00Lunch
14:00-15:00 Colin 14:00-15:00 Biran 14:00-15:00 Frauenfelder
15:00-15:30Coffee break 15:00-15:30Coffee break 15:00-15:30Coffee break
15:30-16:30 Niederkrüger 15:30-16:30 Schwarz 15:30-16:30 Abouzaid
16:30-17:00Coffee break
17:00-18:00 Latschev

(*) All lectures will take place in Bldg NO, 5th floor, "Salle Solvay". (more infos to find your way there)

Abstracts

Mohammed Abouzaid : Homological Mirror Symmetry for Toric varieties and Tropical Geometry

I will describe how to embed the category of coherent sheaves on a smooth projective toric variety in the derived Fukaya category of its mirror. In practice, this means we will study a collection of Lagrangian submanifolds in the cotangent bundle of the torus (satisfying certain boundary conditions) whose Floer complexes (together with the attendant multiplicative structure) is equivalent to Dolbeaut (or Chech) cohomology groups of holomorphic line bundles of the mirror toric variety.

Paul Biran : From uniruled symplectic manifolds to uniruled Lagrangians

In this talk we shall explain a relative version of quantum homology for Lagrangian submanifolds and its algebraic and geometric relation to the usual quantum homology of the ambient symplectic manifold. This makes it possible to transfer geometric properties of the ambient manifold, such as uniruledness, to Lagrangian submanifolds.
We shall present several applications of this point of view, to questions concerning Lagrangian intersections, topology of Lagrangians, and symplectic packing.
Joint work with Octav Cornea.

Vincent Colin : Reeb vector fields and open book decompositions

We determine parts of the contact homology of certain contact 3-manifolds, given a compatible open book decomposition. This is joint work with Ko Honda.

Urs Frauenfelder : On Rabinowitz Floer homology

This is joint work with Kai Cieliebak und Gabriel Paternain. Rabinowitz Floer homology is the semi-infinite dimensional Morse homology for a Lagrange multiplier functional appearing in the work of Rabinowitz. Recently it became possible to extend Rabinowitz Floer homology also to the case of stable Hamiltonian structures which play a major role in Symplectic Field Theory. I will explain the analysis for this extension.

Janko Latschev : Relative contact homology, string topology and the cord algebra

My talk is based on recent joint work with Kai Cieliebak, Tobias Ekholm and Lenny Ng. For a knot in three-space, we show that Lenny's cord algebra is isomorphic to the degree zero relative contact homology of the unit conormal bundle by relating both to a construction in string topology. This point of view also yields a purely topological proof that the cord algebra distinguishes the unknot.

Mark McLean : Exotic Stein manifolds

In each complex dimension greater than two, I will construct infinitely many Stein manifolds diffeomorphic to Euclidean space which are pairwise distinct as symplectic manifolds. I will distinguish them using an invariant called symplectic homology.

Klaus Niederkrüger : Overtwisted in higher dimensions

At the beginning of the talk, I will give the audience the choice between one of the following two topics:
1. Contact homology (and SFT) vanishes for manifolds containing a plastikstufe. I will sketch the proof, and discuss briefly important questions.
2. According to E.Giroux, the negative stabilization of a contact open book (of arbitrary dimension) should give an "overtwisted" contact structure. Such manifolds contain an object that resembles a plastikstufe. I will try to explain what needs to be done to prove that this degenerate plastikstufe also implies non-fillability of the contact manifold.

Leonid Polterovich : An hierarchy of rigid sets in symplectic manifolds.

The talk is based on a joint work with Michael Entov. I discuss an hierarchy of intersection rigidity properties of sets in a closed symplectic manifold: some rigid sets are more rigid than the others. Examples include certain fibers of moment maps of Hamiltonian torus actions, monotone Lagrangian submanifolds as well as certain, possibly singular, sets defined in terms of Poisson-commutative subalgebras of smooth functions.

Dietmar Salamon : Intersection of vanishing cycles and representations of the framed braid group

The framed braid group on m strings acts on the space of distinguished configurations associated to a Lefschetz fibration with m critical values. The action on the intersection matrix of the associated vanishing cycles corresponds to an action of the framed braid group on a suitable space of m x m matrices. This action is generated by a ``Lefschetz monodromy cocycle''. (Joint work with Alexandru Oancea.)

Matthias Schwarz : Products in String Topology via Floer Homology

Floer Homology for cotangent bundles is equivalent to standard homology for path and loop spaces of manifolds. In joint work with A. Abbondandolo we show that this equivalence extends to all product structures currently considered in String Topology.

Jean-Yves Welschinger : Donaldson category for spheres in symplectic manifolds with vanishing first Chern class

I will define the Floer cohomology of two transversal Lagrangian spheres in a symplectic manifold with vanishing first Chern class. The key point is a phenomenon of localization of holomorphic disks sitting on those Lagrangian spheres, observed thanks to symplectic field theory. I will then discuss the product structure on this Floer cohomology and the induced structure of a Donaldson category of spheres.


Registered participants:

  • Jaume Amoros (Universitat Politècnica de Catalunya, Barcelona)
  • Sílvia Anjos (Instituto Superior Técnico, Lisbon)
  • Gabi Ben Simon (ETH Zurich)
  • Patrick Bernard (Université Paris 9)
  • Mélanie Bertelson (Université Libre de Bruxelles)
  • Baptiste Chantraine (Université Libre de Bruxelles)
  • Kai Cieliebak (Ludwig-Maximilians-Universität, Munich)
  • Rémi Crétois (ENS Lyon)
  • Mihai Damian (Université Louis Pasteur, Strasbourg)
  • Jonathan Evans (Cambridge University)
  • Hélène Eynard-Bontemps (ENS Lyon)
  • Emmanuel Ferrand (Université Paris VI)
  • Joel Fine (Université Libre de Bruxelles)
  • Agnès Gadbled (Université Louis Pasteur, Strasbourg)
  • Damien Gayet (Université de Lyon 1)
  • Hansjörg Geiges (Universität zu Köln)
  • Emmanuel Giroux (ENS Lyon)
  • Jesús Gonzalo (Universidad Autónoma de Madrid)
  • Michael Hecht (Universität Leipzig)
  • Muriel Heistercamp (Université Libre de Bruxelles)
  • Sonja Hohloch (Universität Leipzig)
  • Vincent Humilière (Ecole Polytechnique, Palaiseau)
  • Dominic Jänichen (Cambridge University)
  • Will Kirwin (Max Planck Institute, Leipzig)
  • Driton Komani (ETH Zurich)
  • François Laudenbach (Université de Nantes)
  • Laurent Lazzarini (Université Paris 6)
  • Rémi Leclercq (Max Planck Institute, Leipzig)
  • Patrick Massot (ENS Lyon)
  • Klaus Mohnke (Humboldt Universität zu Berlin)
  • Ignasi Mundet i Riera (Universitat de Barcelona)
  • Gregor Noetzel (Max Planck Institute, Leipzig)
  • Emmanuel Opshtein (Université Louis Pasteur, Strasbourg)
  • Andreas Ott (ETH Zurich)
  • Dmitri Panov (Imperial College, London)
  • Federica Pasquotto (Vrije Universiteit Amsterdam)
  • Patrick Popescu-Pampu (Université Paris 7)
  • Francisco Presas (Universidad Complutense de Madrid)
  • Petr Pushkar (Université Libre de Bruxelles)
  • Rares Rasdeaconu (Université Louis Pasteur, Strasbourg)
  • Nicolas Roy (Humboldt Universität zu Berlin)
  • Bijan Sahamie (Universität zu Köln)
  • Nermin Salepci (Université Louis Pasteur, Strasbourg)
  • Sheila Sandon (Instituto Superior Técnico, Lisbon)
  • Felix Schlenk (Université Libre de Bruxelles)
  • Felix Schmäschke (Universität Leipzig)
  • Jan Swoboda (ETH Zurich)
  • Benoit Tonnelier (Ecole Polytechnique, Palaiseau)
  • Alesky Tralle (University of Warmia and Mazury, Olsztyn)
  • Jack Waldron (Cambridge University)
  • Chris Wendl (ETH Zurich)
  • Ingo Wieck (Universität zu Köln)
  • Kai Zehmisch (Universität Leipzig)
  • Mathias Zessin (Université Libre de Bruxelles)

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