# Symplectic Geometry

Organizers: Eleny Ionel, Yasha Eliashberg, Mohammed Abouzaid, and Mohan Swaminathan.

There is tea prior to the talk in the 4th floor lounge.

The Northern California Symplectic Geometry Seminar usually meets on the first Monday of each month, and alternates between Stanford and Berkeley.

## Past Events

In this talk, I will explain how to use (relative) recursion relations in the HOMFLYPT-skein to study skein-valued open Gromov-Witten partition functions as defined by Ekholm and Shende. As a first application, I will prove a crossing formula for partition functions of basic holomorphic disks…

In this talk I will describe an especially simple proof of contact non-squeezing at large scale in R^{2n} \times S^1. The argument (current joint work with Lisa Traynor) was first sketched in a 2016 poster. It uses a persistence-module viewpoint to extract more information from the existing…

Dimitroglou-Rizell-Golovko constructs a family of Legendrians in prequantization bundles by taking lifts of monotone Lagrangians. These lifted Legendrians have a Morse-Bott family of Reeb chords. We construct a version of Legendrian Contact Homology(LCH) for Rizell-Golovko's lifted Legendrians…

In this talk, I will review the concept of fixed point Floer (co)homology and its product and coproduct structure. I will explain the concrete computation of the product and coproduct structures for iterations of a single Dehn twist on a symplectic surface with genus at least two. As an…

*Abstract: *Consider a Liouville domain D embedded in a closed symplectic manifold M. To D one can associate two types of Floer theoretic invariants: intrinsic ones like the wrapped Fukaya category which depend on D only, and relative ones which involve both D and M. It is often the case…

Generating families (generating functions) for exact Lagrangian or Legendrian submanifolds provides a finite dimensional approach to understanding nonclassical invariants of the submanifolds. Given an exact Lagrangian cobordism between Legendrians in 1-jet bundles, we prove that a generating…

An exact Lagrangian L in a cotangent bundle T*Q is a nearby fibre if it agrees with a cotangent fibre at infinity and it is disjoint from another cotangent fibre. The projection from T*Q to Q induces a map from L/\partial L to Q. We will show that this map is null-homotopic after…

*Abstract: *The small quantum connection on a monotone symplectic manifold M is one of the simplest objects in enumerative geometry. Nevertheless, the poles of the connection have a very rich structure. After reviewing this background, I will outline a proof that, under suitable…

*Abstract:* Sectorial descent, established in earlier work with Pardon-Shende, gives a local-to-global formula computing the wrapped Fukaya category of a Weinstein manifold from a sectorial cover. If one has a specific fixed global Lagrangian in mind that isn't contained in a single…

I will discuss joint work with Luya Wang on the other direction of the Donaldson 4-6 problem. Specifically, we show that any two simply-connected symplectic 4-manifolds, whose products with S^2 are deformation equivalent, have the same Gromov-Witten invariants. The proof relies on a…