What analysis, combinatorics, and quilted spheres can tell us about symplectic topology

by Nate Bottman (Max Planck Institute, Bonn)

Tuesday 11 Jun 2024, 05:00 → 06:00 Europe/Berlin

H4 (Geom)

Abstract: 
A central tool for studying symplectic manifolds is the Fukaya category. In this talk, I will describe a program, which is ongoing joint work with Katrin Wehrheim, to relate the Fukaya categories of different symplectic manifolds via a structure called the "symplectic (A-infinity,2)-category". The key objects are "witch balls", which are pseudoholomorphic maps whose domain is the Riemann sphere decorated with circles and points, and "2-associahedra", the configuration spaces of these domains. I will describe applications to symplectic topology, and explain how my work enables a unified, functorial version of Kontsevich's Homological Mirror Symmetry conjecture.