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Séance du 6 novembre 2015

Lieu: IHP, salle 01** **

**11:00 ** Jonny Evans (Londres)** **
**Generating Fukaya categories of Hamiltonian G-manifolds****. **
*Abstract:* Joint work with YankI Lekili. We use quilted Floer theory
to study Lagrangian orbits of Hamiltonian group actions. As a
consequence we can deduce that toric fibres split-generate the
Fukaya category of a toric Fano manifold, as well as some generation
results in the presence of nonabelian group actions. One corollary
is that the quantum cohomology A_\infty-algebra of a toric Fano
manifold cannot be formal if the underlying quantum cohomology ring
is not semisimple.

**14:15 ** John Pardon (Stanford/IHES)
**Contact homology and virtual fundamental cycle**
*Abstract: *Contact homology is a powerful invariant of contact
manifolds introduced by Eliashberg--Givental--Hofer. The definition
involves certain counts of pseudo-holomorphic curves, however these
are usually only "virtual" counts since the moduli spaces of such
curves are often not cut out transversally. I will discuss one way to
construct these counts rigorously.
**16:00 ** Penka Georgieva (Jussieu)** **
**Real Gromov-Witten theory in all genera**
*Abstract:* We construct positive-genus analogues of Welschinger's invariants for many real symplectic manifolds, including the odd-dimensional projective spaces and the quintic threefold. Our approach to the orientability problem is based entirely on the topology of real bundle pairs over symmetric surfaces. This allows us to endow the uncompactified moduli spaces of real maps from symmetric surfaces of all topological types with natural orientations and to verify that they extend across the codimension-one boundaries of these spaces. In reasonably regular cases, these invariants can be used to obtain lower bounds for counts of real curves of arbitrary genus. Joint work with A. Zinger.

Prochaines
séances: 04/12 (G. Cazassus, A. Chiodo. O. Fabert)
Autre activité symplectique à Paris: groupe de travail faisceaux.
Mini-cours de John Pardon à l'IHES