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