Lieu: IHP, salle 201.
11:00 Stephan Mescher (Leipzig)
Topological complexity of symplectic manifolds
Abstract: Topological complexity (TC) was introduced by M. Farber as a numerical homotopy invariant motivated by the motion planning problem from robotics. It bears similarity with the Lusternik-Schnirelmann category. In this talk, I will present a result from joint work with Mark Grant in which we identify a topological condition on a symplectic manifold that ensures TC to coincide with a standard dimensional upper bound. This result is the TC analogue of a theorem by Rudyak-Oprea on the Lusternik-Schnirelmann category of symplectically aspherical manifolds.
After an introduction to TC and the presentation of some basic results, I will explain how the cohomology groups of a space may be used to derive lower bounds on TC. I will then outline how these bounds are combined with infinite-dimensional de Rham theory to provide the abovementioned result for symplectic manifolds.
14:15 Gabriele Benedetti (Heidelberg)
A local systolic inequality for odd-symplectic forms on circle bundles
Abstract: We study a generalization of the local contact systolic inequality to odd-symplectic forms on circle bundles over closed symplectic manifolds. We establish the inequality, when the symplectic manifold has dimension two and give some application to the study of closed magnetic geodesics on surfaces. This is joint work with Jungsoo Kang from Seoul National University.
16:00 Penka Georgieva (Jussieu).
The local real Gromov-Witten theory of curves.
Abstract:The local Gromov-Witten theory of curves studied by Bryan and Pandharipande revealed strong structural results for the local GW invariants, which were later used by Ionel and Parker in the proof of the Gopakumar-Vafa conjecture. In this talk I will report on a joint work with Eleny Ionel on the extension of these results to the real setting. Similarly to the classical case, we obtain a complete solution in terms of representation theoretic data using the formalism of (an extension of) a Klein TQFT. The local real version of the Gopakumar-Vafa formula is obtained as a corollary.
Prochaines séances: 10/05 (Nonenmacher, Salamon, Vertesi), Séance du 14/06 annulée (exposé de L. Macarini reporté).
Autre activité symplectique à Paris:
Séminaire Nantes-Orsay
