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.
Upcoming Events
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…
Abstract
Past Events
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: 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…
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…
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…
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…