Northern California Symplectic Seminar
Upcoming Events
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…
Abstract: Around 2000, Biran introduced the notion of polarization of a symplectic manifold, and showed that the associated Lagrangian skeleta exhibit remarkable rigidity properties. He proved in particular that their complements may have small Gromov width. In this…
Past Events
Abstract: Take an irrational rotation of the two-sphere; it only has the north and south poles as its periodic points. However, Franks proved that for any area-preserving diffeomorphism of the two-sphere, if it has more than two fixed points, then it must have infinitely many periodic…
Abstract: In recent years several groups of authors introduced various invariants that are based on Lagrangian Floer homology of a symmetric product of a symplectic manifold. In this talk, I will introduce Heegaard Floer symplectic cohomology (HFSH), an invariant of a Liouville domain M…
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…
Abstract: The moduli space of closed holomorphic curves in a closed symplectic manifold can be compactified using stable maps. However, even in the nicest of situations (e.g., degree d curves of genus g in a complex projective space, with d .. g), counting dimensions shows that most stable maps…
Abstract: This is joint work in progress with Dan Cristofaro-Gardiner. We explore the topological dynamics of Reeb flows beyond periodic orbits and find the following rather general phenomenon. For any Reeb flow for a torsion contact structure on a closed 3-manifold, any point is arbitrarily…
Distinct Hamiltonian isotopy classes of Lagrangian tori in $\mathbb{CP}^2$ can be associated to Markov triples. With two exceptions, each of these tori are symplectomorphic to exactly three Hamiltonian isotopy classes of tori in the ball (the affine part of $\mathbb{CP}^2$). We investigate…
Abstract: In his seminal 2001 paper, Biran introduced the concept of Lagrangian Barriers, a symplectic rigidity phenomenon coming from obligatory intersections with Lagrangian submanifolds which don't come from mere topology.
In this joint work with Richard Hind and Yaron Ostrover, we…
In the late '90s, Eliashberg and Thurston established a remarkable connection between foliations and contact structures in dimension three: any co-oriented, aspherical foliation on a closed, oriented 3-manifold can be approximated by positive and negative contact structures.…
This talk will present recent advances on the study of embedded exact Lagrangians in the standard Darboux 4-ball. We will discuss a three step strategy to classify Hamiltonian isotopy classes of Lagrangian fillings of Legendrian links. The main results for the two first steps, existence and…