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

Brayan Ferreira (Instituto de Matemática Pura e Aplicada): 

Gromov Width of Disk Cotangent Bundles of Spheres of Revolution: The question of whether a Symplectic manifold embeds into another is central in Symplectic topology. Since Gromov nonsqueezing theorem, it is known that this is a different problem from volume preserving embeddings. Symplectic capacities are invariants that give obstructions to symplectic embeddings. The first example of a symplectic capacity is given by the Gromov width, which measures the biggest ball that can be symplectically embedded into a symplectic manifold. In this talk, we are going to discuss the Gromov width for the example of disk cotangent bundles of spheres of revolution. The main results are for the Zoll cases and for the case of ellipsoids of revolution. The main tools are action angle coordinates (Arnold-Liouville theorem) and ECH capacities. This is joint work with Alejandro Vicente and Vinicius Ramos.

Roman Krutowski (University of California, Los Angeles):

Maslov Index Formula in Heegaard Floer Homology: The formula introduced by Robert Lipshitz for Heegaard Floer homology is now one of the basic tools for those working with HF homology. The convenience of the formula is due to its combinatorial nature. In the talk, we will discuss the recent combinatorial proof of this formula.

Amanda Hirschi (University of Cambridge): 

Global Kuranishi Charts for Gromov-Witten Moduli Spaces and a Product Formula: I will describe the construction of a global Kuranishi chart for moduli spaces of stable pseudoholomorphic maps of any genus and explain how this allows for a straightforward definition of GW invariants. For those not convinced of its usefulness, I will sketch how this can be used to obtain a formula for the GW invariants of a product. This is joint work with Mohan Swaminathan.