Topology Seminar (Introductory Talk): Quilts, operads, and the Fukaya category

Seminar | November 7 | 2-3 p.m. | 736 Evans Hall

 Nate Bottman, Princeton University

 Department of Mathematics

In my first talk, I will introduce the Fukaya category of a compact symplectic manifold. This is an invariant that keeps track of the Lagrangian submanifolds, as well as an intersection theory of these submanifolds that is enhanced by counts of pseudoholomorphic polygons. The algebraic structure of the Fukaya category is controlled by a collection (in fact, an operad) of polytopes called associahedra, which are compactified moduli spaces of points on the real line. Finally, I will describe the theory of pseudoholomorphic quilts, introduced 10 years ago by Wehrheim and Woodward, which provides an elegant framework for relating Fukaya categories of different symplectic manifolds. There will be many pictures along the way, and I will assume no symplectic background.