Northern California Symplectic Seminar

Given a smooth closed n-manifold M and a k-tuple of basepoints in M, we define a Morse-type A∞-algebra called the based multiloop A∞-algebra and show the equivalence with the higher-dimensional Heegaard Floer A∞-algebra of k disjoint cotangent fibers of T*M.

Symplectic cohomology is a fundamental invariant of a symplectic manifold M with contact type boundary that is defined in terms of dynamical information and counts of pseudoholomorphic genus zero curves, and carries algebraic structures that parallel the algebraic structures on the Hochschild (…

Abstract: Every Anosov flow on a closed oriented three-manifold gives rise to a four-dimensional

Liouville domain, whose Liouville homotopy class depends only on the homotopy class of the

Anosov flow. The goal of this talk is to explain this construction and discuss geometric…

Abstract: We define the K-theoretical virtual fundamental cycle of an almost complex global

Kuranishi atlas, as an element in the (analytic) orbifold K-homology of the base space of the

atlas, and verify that it defines the same K-theoretical Gromov-Witten invariants as in Abouzaid…

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…

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…