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

Locally conformally symplectic (LCS) manifolds are generalisations of symplectic manifolds where the 2-form is not closed but instead satisfies the identity dω = η ∧ ω for a closed 1-form η. The study of these manifolds is equivalent to that of...

Given a symplectic 4-manifold it may admit multiple toric fibrations. These can be seen as boundary points of the moduli space of almost toric fibrations. We will sketch that all toric fibrations are in the same connected component of this moduli...

I'll introduce the genus zero open Gromov-Witten invariants for even-dimensional Lagrangians. The definition relies on a canonical family of bounding cochains satisfying the point-like condition of Solomon-Tukachinsky, with non-commutative...

Helicity is an invariant of divergence free vector fields on a three-manifold. One of its fundamental properties is invariance under volume preserving diffeomorphisms. Arnold, having derived an ergodic interpretation of helicity as an asymptotic...

I will begin by motivating the study of invariant distances on spaces of Legendrians. I will then discuss two main results:
(a) the construction of a new unbounded invariant distance on the universal cover of many Legendrian isotopy classes ;
(b) the...

A convex toric domain  is a 4-dimensional subset of , defined as the preimage of a bounded convex region  in the positive quadrant of  under the moment map. We consider how geometric features of  such as the curviness of its boundary and its affine...

Given a Morse-Smale pair on a manifold M, it is possible to entirely recover its fundamental group in a combinatorial manner. We call this construction the Morse fundamental group. Motivated by a similar construction of a « Floer fundamental group »...

Lagrangian Floer theory is useful to detect non-displaceability of Lagrangian submanifolds via Hamiltonian isotopies. A related question, in the presence of a group action, is whether a certain Lagrangian is equivariantly displaceable, that is by a...

The Birkhoff attractor is a closed invariant subset associated with any dissipative twist map of the annulus (of dimension 2), which was introduced by Birkhoff in 1932. We will see that it can be generalized to higher dimensions using tools from...

The symplectic area of a Lagrangian submanifold L in a symplectic manifold is defined as the minimal positive symplectic area of a smooth 2-disk with boundary on L. A Lagrangian torus is called extremal if it maximizes the symplectic area among all...