Lieu: IHP, Amphi Darboux.
11:00 Eleny Ionel (Stanford)
Thin compactifications and Relative Fundamental Classes.
Abstract: Families of moduli spaces in symplectic Gromov-Witten theory and gauge theory are often manifolds that have "thin" compactifications, in the sense that the boundary of the generic fiber has codimension at least two. In this talk we discuss a notion of a relative fundamental class for such thinly compactified families. It associates to each fiber, regardless whether it is regular or not, an element in its Cech homology in a way that is consistent along paths. The invariants defined by relative fundamental classes agree with those defined by pseudo-cycles, and the relative fundamental class is equal to the virtual fundamental class defined by Pardon via implicit atlases in all cases when both are defined. We give some examples of this construction, discuss some of its properties, and its benefits. This talk is based on joint work with Tom Parker..
14:15 Cedric De Groote (MPI Leipzig)
Orderability up to conjugation of certain open contact manifolds.
Abstract: Eliashberg and Polterovich introduced in 2000 a notion of orderability for the group of contact isotopies of a contact manifold, which provides insights into the geometry of that group. Later, this same notion “up to conjugation” was used by Borman, Eliashberg and Murphy in their proof of the flexibility of overtwisted contact structures in all dimensions. I will review some of the history of that problem, and then present a new result on the orderability up to conjugation of certain contact annuli. This involves restating the problem as a contact non-squeezing result, which is then shown using a version of contact homology.
16:00 Zhengi Zhou (IAS)
Symplectic fillings of asymptotically dynamically convex manifolds.
Abstract: I will introduce the concept of k-dilation on symplectic cohomology, which generalizes the vanishing of symplectic cohomology and symplectic dilation. The existence of k-dilation is independent of certain fillings for a class of contact manifolds admitting only the trivial augmentation, called asymptotically dynamically convex manifolds. Then I will derive some consequences on uniqueness and existence of fillings, embeddings, and cobordisms.
Prochaines séances: probable annulation...
Autre activité symplectique à Paris:
Séminaire Nantes-Orsay
