***** ATTENTION: LIEU INHABITUEL *****

**11:00**Chris Wendl (Londres) :

When is a Stein structure merely symplectic?

Résumé:

The study of Stein manifolds and their symplectic geometry has
increasingly been dominated by the question of "rigid vs. flexible",
e.g. subcritical Stein manifolds satisfy an h-principle, so their Stein
homotopy type is determined by the homotopy class of the almost complex
structure. I will show that in dimension 4, there is a much larger
class of Stein domains that exist somewhere between rigid and flexible:
while the h-principle does not hold in a strict sense, their Stein
deformation type is completely determined by their symplectic
deformation type. This result depends on some joint work with Sam Lisi
and Jeremy Van Horn-Morris involving the relationship between Stein
structures and Lefschetz

fibrations, which can sometimes be realised as foliations by J-holomorphic curves.

**14:15**Grigory Mikhalkin (Génève & FSMP) :

Volumes of amoebas.

Résumé: We consider a higher-dimensional generalization of the Passare-Rullgård theorem providing an upper bound for the area of a planar amoeba (the logarithmic image of a complex algebraic variety).

**15:45**Alexander Ritter (Oxford) :

Symplectic cohomology and circle-actions.

Résumé: I will explain how to compute the symplectic cohomology of a manifold M conical at infinity, whose Reeb flow at infinity arises from a Hamiltonian circle-action on M. For example, this allows one to compute the symplectic cohomology of negative line bundles in terms of the quantum cohomology. In joint work with Ivan Smith, we showed that via the open-closed string map this determines the wrapped Fukaya category of negative line bundles over projective space, which involves the existence of a non-displaceable monotone Lagrangian torus.

Prochaines séances: 10/01, 07/03, 04/04