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

Benoît Joly (Ruhr-Universität Bochum), Barcodes for Hamiltonian homeomorphisms of surfaces

In this talk, we will study the Floer Homology barcodes from a dynamical point of view. Our motivation comes from recent results in symplectic topology using barcodes to obtain dynamical results. We will give the ideas of new constructions of barcodes for Hamiltonian homeomorphisms of surfaces using Le Calvez's transverse foliation theory. The strategy consists in copying the construction of the Floer and Morse Homologies using dynamical tools like Le Calvez's foliations.

Marco Castronovo (Columbia University), Polyhedral Liouville domains

I will explain the construction of a new class of Liouville domains that live in a complex torus of arbitrary dimension, whose boundary dynamics encodes information about the singularities of a toric compactification. The primary motivation for this work is to find a symplectic interpretation of some curious Laurent polynomials that appear in mirror symmetry for Fano manifolds; it also potentially opens a path to bound symplectic capacities of polarized projective varieties from below.

Agniva Roy (Georgia Institute of Technology), Constructions of High Dimensional Legendrians and Isotopies

I will talk about an ongoing project that explores the construction of high dimensional Legendrian spheres from supporting open books and contact structures. The input is a Lagrangian disk filling of a Legendrian knot in the binding. We try to understand the relationship between different constructions from the same input, and suggest parallels, in the $S^{2n+1}$ case, to a construction defined by Ekholm for $\mathbb{R}^{2n+1}$.