Algebra/Topology seminar

Factorization homology is a type of generalized homology theory. Its coefficients are E_n-algebras in some higher symmetric monoidal category, and it can be evaluated on n-dimensional manifolds. One case relevant in quantum topology is the factorization homology of E₂-algebras in linear categories which are exactly braided monoidal categories (sources include certain Hopf algebras and vertex operator algebras); this case was investigated in detail by Ben-Zvi-Brochier-Jordan. In my talk, I will explain how factorization homology, together with Costello's concept of the derived modular envelope, can be used to set up a general skein theory for cyclic framed E₂-algebras. Moreover, I will outline the classification of modular functors (consistent systems of mapping class group representations) via factorization homology. This is based on different joint projects with Adrien Brochier (IMJ-PRG) and Lukas Müller (Perimeter).