# Program*

15 Feb. 16 Feb. 17 Feb.
9:00-11:00 Accueil,
first discussions...
9:00-10:00 Cieliebak 9:00-10:00 Lisca
10:00-10:30Coffee break 10:00-10:30Coffee break
10:30-11:30 Ekholm 10:30-11:30 Ferrand
12:00-14:00Lunch 12:00-14:00Lunch 12:00-14:00Lunch
14:00-15:00 Schlenk 14:00-15:00 Mohnke 14:00-15:00 Geiges
15:00-15:30Coffee break 15:00-15:30Coffee break 15:00-15:30Coffee break
15:30-16:30 Smith 15:30-16:30 Bernard 15:30-16:30 Cornea
16:30-17:00Coffee break 16:30-17:00Coffee break
17:00-18:00 Giroux 17:00-18:00 Damian

(*) All lectures will take place in Bat. M2, first floor, "Salle de Réunion". (more infos to find your way there)

# Abstracts

Patrick Bernard: Symplectic aspects of Mather Theory.

Kai Cieliebak: A Floer homology for exact contact embeddings.

An exact contact embedding is an embedding of a contact manifold into an exact symplectic manifold such that the restriction of the Liouville 1-form defines the given contact structure. In joint work with Urs Frauenfelder we associate to this situation a Floer homology for a suitable Lagrange multiplier action functional, which vanishes if the image of the embedding is Hamiltonian displaceable. As a consequence, we obtain obstructions to the existence of exact contact embeddings. For example, the unit cotangent bundle of a sphere of dimension greater than three admits no exact contact embedding into a subcritical Stein manifold. This generalizes Gromov's result that there are no exact Lagrangian spheres in linear symplectic space.

Octav Cornea: Quantum structures for monotone Lagrangians.

This talk is based on joint work with Paul Biran. I will discuss some algebraic structures associated to monotone Lagrangian which are defined in terms of the combinatorics of pseudo-holomorphic disks with boundary on the Lagrangian. Among applications I will mention some Lagrangian packing estimates.

Mihai Damian: Floer Novikov homology in the cotangent bundle.

We define a Floer-type homology HF(L, \phi_{t}(L)) where $\phi_{t}$ is a symplectic non-Hamiltonian isotopy on $T^*M$. We infer some results about the topology of exact Lagrangian embeddings $L\subset T^*M$.

Tobias Ekholm: A surgery exact sequence in linearized contact homology.

We present a long exact sequence which connects the linearized contact homology of a contact manifold with Legendrian sphere, the cyclic contact homology of this Legendrian sphere, and the linearized contact homology of the contact manifold which results after surgery on the Legendrian sphere. The talk reports on joint work with Bourgeois and Eliashberg.

Emmanuel Ferrand: Legendrian knots and classical knots

Since the seminal work of Bennequin, a motivation for the study of Legendrian knots can be found in some "classical" knot theory problems. I will review some recent results in this vein by L. Ng, D. Rutherford and others, and discuss some open problems and conjectures.

Hansjörg Geiges: A Bernstein problem for contact spheres.

This is a report on joint work with Jes\'us Gonzalo. We show how certain families of contact structures on a 3-manifold M give rise to a hyperkähler metric on $M\times{\mathbf R}$. The Bernstein problem concerns the completeness of such metrics. I shall discuss how the Gibbons-Hawking ansatz can be used to settle this question.

Emmanuel Giroux: Symplectic mapping classes and fillings

Paolo Lisca: Stein fillability and genus one open books.

In 3-dimensional contact topology one would like to deduce interesting properties of a contact structure from the monodromy of a compatible open book. By recent results due independently to Honda-Kazez-Matic and Baldwin, when the page of the open book has genus one and a single boundary component, the monodromies giving rise to tight contact structures can be explicitely described. After recalling the necessary background and stating the above results, I will talk about work in progress on the problem of characterizing the monodromies of such genus one open books which give rise to Stein fillable contact structures.

Klaus Mohnke: TBA

Felix Schlenk: Lagrangian tori in tame symplectic manifolds.

We study Lagrangian tori in tame symplectic manifolds up to symplectomorphism. In most cases, the tori are local in the sense that they sit in a Darboux chart. We are mostly interested in the monotone case. By refining Chekanovs construction in C^n we first construct non-split monotone tori with prescribed area class. We then prove that many of these tori - seen in any tame symplectic manifold with sufficiently large Gromov width - are different. E.g., in CP^n we find \approx 2^n different monotone tori. This is joint work with Yura Chekanov.

Ivan Smith: Exact Lagrangian submanifolds revisited.

I will report on joint work-in-progress with Kenji Fukaya and Paul Seidel, in which we use ideas from homological mirror symmetry to derive new constraints on exact Lagrangian submanifolds in cotangent bundles.

# Registered participants:

• Michèle Audin (ULP, Strasbourg),
• Mhamed Beghdadi (Royal Institute of technology),
• Raouf Dridi (USTL, Villeneuve D\'Ascq),
• Jonathan Evans (Cambridge),
• Hélène Eynard-Bontemps (ENS Lyon),
• Oliver Fabert (LMU Munich/ETH Zurich),
• Muriel Heistercamp (Université Libre de Bruxelles),
• Vincent Humiliere (Ecole Polytechnique),
• Hassan Ait Haddou (LAMAV Université de Valenciennes),
• Viatcheslav Kharlamov (ULP, Strasbourg),
• Otto van Koert (Université Libre de Bruxelles),
• Francois Laudenbach (Faculte des sciences, Universite de Nantes),
• Laurent Lazzarini (Paris 7),
• Rémi Leclercq (Université de Montréal),
• Alessia Mandini (University of Bologna),
• Patrick Massot (ENS Lyon),
• Mark McLean (Cambridge),
• Klaus Niederkrüger(Université Libre de Bruxelles),
• Dr. Chayan Kumar Mishra (Dept. Of Maths&Stats.,Dr.RML Avadh University),
• Andreas Ott (ETH Zurich),
• Dmitri Panov (Imperial London College),
• Federica Pasquotto (Vrije Universiteit Amsterdam),
• Patrick Popescu-Pampu (Paris 7),
• Nicolas Roy (Humboldt University),