Higher Structures @ Centre international de rencontres mathématiques (CIRM), Luminy

Title
Configuration spaces and operads
Event
Higher Structures
Location
Centre international de rencontres mathématiques (CIRM), Luminy
On

Abstract

Configuration spaces consist of tuples of pairwise distinct points in a given space. Studying the homotopy type of configuration spaces of manifolds is a classical problem in algebraic topology. In this talk, I will explain how to use the theory of operads - more precisely, Kontsevich’s proof of the formality of the little disks operads - to obtain results on the real homotopy type of configuration spaces of simply connected closed smooth manifolds. I will also talk about generalizations and applications: manifolds with boundary, framed configuration spaces, factorization homology, and work in progress on complements of submanifolds.