Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

Adrien Currier (Université de Nantes) : Exact Lagrangians in Cotangent Bundles with Locally Conformally Symplectic Structure

First considered by Lee in the 40s, locally conformally symplectic (LCS) geometry appears as a generalization of symplectic geometry which allows for the study of Hamiltonian dynamics on a wider range of manifolds while preserving the local properties of symplectic geometry. After a long period of hibernation (especially as far as the topological aspect is concerned), interest in this subject has picked up again recently. However, to this day, the field of LCS topology remains vastly unexplored.
In this talk, we will introduce the various objects of LCS geometry and their behavior through both definitions and examples. We will also explore some questions around an LCS version of the nearby Lagrangian conjecture and some of the connections between LCS and contact geometry.

Adi Dickstein (Tel Aviv University) : Relative Symplectic Cohomology of Pairs

Relative symplectic cohomology, an invariant of subsets in a symplectic manifold, was recently introduced by Varolgunes. In this talk, I will present a generalization of this invariant to pairs of subsets, which shares similar properties with the singular cohomology of pairs, such as excision and a product structure. Using this new invariant, I will demonstrate new symplectic rigidity phenomena. Joint with Yaniv Ganor, Leonid Polterovich and Frol Zapolsky.

Elliot Gathercole (Lancaster University): Superheavy Skeleta for Non-Normal Crossings Divisors 

Given an anticanonical divisor in a projective variety, one naturally obtains a monotone Kähler manifold, and the divisor complement is naturally a Liouville manifold. For certain kinds of singular divisors, we will outline a result obtaining rigid (in particular, superheavy) neighbourhoods of the Lagrangian skeleton of the complement, of prescribed volume dependent on the divisor, and illustrate this with some interesting examples where the skeleton itself is superheavy.