Bonn Topology Group - Abstracts

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Talk

June 18, 2024
Nate Bottman (Max Planck Institute for Mathematics): What analysis, combinatorics, and quilted spheres can tell us about symplectic topology

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.

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