Miguel Abreu: Toric Kähler-Sasaki geometry in action-angle coordinates

In the same way that a contact manifold determines and is determined by a symplectic cone, a Sasaki manifold determines and is determined by a Kähler cone. Kähler-Sasaki geometry is the geometry of such a pair.

In this talk, after a brief introduction, I will present the Burns-Guillemin-Lerman and Martelli-Sparks-Yau generalization to toric Kähler-Sasaki geometry of the action-angle coordinates approach to toric Kähler geometry. I will then show how this approach can be used to relate a recent new family of Sasaki-Einstein metrics constructed by Gauntlett-Martelli-Sparks-Waldram in 2004, to an old family of extremal Kähler metrics constructed by Calabi in 1982.

Peter Albers: Leaf-wise intersections and Rabinowitz Floer homology

This is joint work with Urs Frauenfelder. We address the leaf-wise intersection problem for hypersurfaces of restricted contact type. This problem originates from work of Moser in 1978. We show how critical points of a perturbed Rabinowitz action functional give rise to a solution of this problem. From this we derive existence results for Hofer-small Hamiltonian diffeomorphism. If the Rabinowitz Floer homology does not vanish we obtain existence results for general Hamiltonian diffeomorphisms.

Baptiste Chantraine: Non-symmetry of Lagrangian concordance

After giving the definition of two new relations on the set of Legendrian knots up to isotopy, namely Lagrangian cobordism and Lagrangian concordance, we will show with the help of an explicit example that the latter is non-symmetric.

Paolo Ghiggini: Giroux torsion, twisted coefficients and applications

The Giroux torsion of a contact 3-manifold is a measure of how much the contact planes rotate in the neighbourhood of an embedded torus. After introducing the main properties of Heegaard Floer homology with twisted coefficients, I will describe how Giroux torsion influences the contact invariant in Heegaard Floer homology, and I will apply the result to the classification of tight contact structures on the boundary of the Gompf nuclei - Σ (2,3,6n-1) for n>2.

Vincent Humilière: The Calabi invariant for some homeomorphisms

The Calabi invariant is an interesting group homomorphism defined on the Hamiltonian group of non-compact symplectic manifolds. Although this homomorphism is not continuous for C⁰ topology, we shall see that it can be extended to some groups of homeomorphisms, with the help of some symplectic rigidity results.

Ludmil Katzarkov: Superschemes homological mirror symmetry and applications

In this talk we will look at some clasical questions in algebraic geometry from a new perspective.

François Lalonde: On the group of Hamiltonian diffeomorphisms that preserve a Lagrangian submanifold: a relative Seidel morphism and the Albers map

Given a Lagrangian submanifold L in a symplectic manifold M, we define a relative Seidel morphism in the following way: to each path of Hamiltonian diffeomorphisms of M starting at the identity and ending at one preserving L, we assign an invertible element of the Floer homology of L. We show that this is compatible with the usual absolute Seidel morphism through the Albers map relating FH(M) and FH(L). This actually fits in two exact sequences, one at the level of homotopy groups of the relevant Hamiltonian diffeomorphisms, the other at the level of the various Floer homologies, the two sequences being related by the appropriate Seidel morphims. Joint work with Shengda Hu.

Gabriel Paternain: Symplectic topology of Mañé's critical values

Consider a closed Riemannian manifold M and let σ be a closed 2-form whose pull-back to the universal covering of M is exact. I will discuss the changes in the symplectic topology of a hypersurface |p|²=2k in the twisted cotangent bundle determined by σ as k makes its transition from high energies to low energies. It has been known for some time (Aubry-Mather theory) that drastic changes in the dynamical properties of the hypersurface take place at Mañé's critical values. I will try to relate these phase transitions to symplectic properties like displacement, stability and vanishing of the Rabinowitz Floer homology. This is joint work with Kai Cieliebak and Urs Frauenfelder.

Francisco Presas: Non-fillability vs non-squeezing in contact geometry

We review the constructions of non-fillable contact manifolds discovered in the last few years. We add a new one: GPS structures. Then, we relate them to the non-squeezing results due to Eliashberg-Kim-Polterovich. In particular, we sketch a proof of the orderability of the overtwisted contact manifolds.

Jake Solomon: Real symmetry and mirror symmetry

András Stipsicz: Combinatorial description of the U²=0 Heegaard Floer groups

We show that every 3-manifold admits a Heegaard diagram in which a truncated version of Heegaard Floer homology (when the holomorpic disks pass through the basepoints at most once) can be computed combinatorially. The construction relies on the fact that a closed 3-manifold can be given as a triple branched cover of S³ along a link.