GP Seminar: Fukaya categories and bordered knot Floer homologies

According to a proposal of Aganagic, knot invariants and their categorifications can be defined using symplectic geometry in two different ways, via the equivariant Fukaya category of a holomorphic symplectic manifold, or the absolute Fukaya category of a half-dimensional real symplectic manifold obtained by reduction. In this talk, we will be focusing on the case of the torus equivariant Fukaya category of a hypertoric variety, and the absolute Fukaya category of the complement of a hyperplane arrangement in the complex vector space. The study of these Fukaya categories recovers the Ozsvath-Szabo algebra and relates to various conjectures of representation theorists. This is based on joint works (in progress) with Sukjoo Lee, Siyang Liu and Cheuk-Yu Mak.

This is a seminar in the Centre of Geometry and Physics seminar series.