|31 Jan.||1 Feb.||2 Feb.|
|10:00-10:30||Coffee break||10:00-10:30||Coffee break|
|15:00-15:30||Coffee break||15:00-15:30||Coffee break||15:00-15:30||Coffee break|
(*) All lectures will take place in Bldg NO, 5th floor, "Salle Solvay". (more infos to find your way there)
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.