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Symplectic geometry and topology

01 Sep - 11 Dec 2015

The main seminars are held on Tuesdays and Thursdays.

Tuesday October 13

14:00 - 15:00 Georgios Dimitroglou Rizell, University of Cambridge

Floer homology for Lagrangian cobordisms

Abstract: Legendrian contact homology (LCH) is a Legendrian isotopy invariant. We introduce a version of wrapped Floer homology for pairs of Lagrangian cobordisms having Legendrian ends that admit augmentations. This theory is used to establish long exact sequences involving the singular homology of a Lagrangian cobordism and the linearised LCH of its Legendrian ends. As an application we show that an exact Lagrangian cobordism from a Legendrian sphere to itself necessarily is a concordance in high dimensions. This is joint work with B. Chantraine, P. Ghiggini and R. Golovko.

15:30 - 16:30 Baptiste Chantraine, Université de Nantes

Legendrian contact homology and positive isotopies

Abstract: A positive Legendrian isotopy in a contact manifold is a Legendrian isotopy such that the Legendrian submanifold always moves in the direction positively transverse to the contact distribution. Such an isotopy presents behaviours similar to propagating waves. In this talk we will describe how to find obstructions to the existence of a positive Legendrian loop in some cases using the Floer theory for Lagrangian cobordisms developed with G. Dimitroglou Rizell, P. Ghiggini and R. Golovko. As a concrete application we will give a new proof of the fact that hypertight contact manifolds are orderable. This is a joint work with Vincent Colin.

Thursday October 15

14:00 - 15:00 Michael Entov, Technion - Israel Institute of Technology

Connecting trajectories of Hamiltonian flows

Abstract: The talk, based on a joint work with L.Polterovich, will address the following basic question of Hamiltonian dynamics: given a (time-dependent) Hamiltonian, is there a trajectory of its flow connecting two given sets? I will discuss a new method of proving the existence of such chords, based on an old construction of Mohnke who used it at the time to prove Arnold's Chord Conjecture, and various open questions related to it.

15:30 - 16:30 Michael Sullivan, University of Massachusetts

Cellular homology, augmentations and generating families for Legendrian surfaces

Abstract: Given a Legendrian surface in a contact one jet space, there is a local combinatorial DGA associated to the cell decomposition of the base projection of the Legendrian. The DGA is quasi-isomorphic to the Legendrian contact DGA. Using this reformulation I show how a generating family for the Legendrian  produces an augmentation for the DGA. I will also sketch a partial converse. This is joint work with Dan Rutherford.