# Points and lines

 Members' Seminar Topic: Points and lines Speaker: Nathaniel Bottman Affiliation: Member, School of Mathematics Date: Monday, December 12 Time/Room: 1:15pm - 2:15pm/S-101 Video Link: https://video.ias.edu/membsem/2016/1212-NathanielBottman

The Fukaya category of a symplectic manifold is a robust intersection theory of its Lagrangian submanifolds. Over the past decade, ideas emerging from Wehrheim--Woodward's theory of quilts have suggested a method for producing maps between the Fukaya categories of different symplectic manifolds. I have proposed that one should consider maps controlled by compactified moduli spaces of marked parallel lines in the plane, called "2-associahedra". In this talk I will describe the 2-associahedra, with a focus on their topological and combinatorial aspects; in particular, I will produce combinatorial data that are in bijection with the strata of the 2-associahedra, and describe a generating function technique for computing the number of dimension-$m$ strata in a particular 2-associahedron. I will not assume any familiarity with symplectic geometry.