There is a relationship between higher algebra/category theory and differential topology. Evidence of this is abundant. For instance, Khovanov homology can be regarded as a knot invariant obtained from a suitable representation of a quantum group, the collection of which forms a braided monoidal category. Also, Turaev-Viro 3-manifold invariants are constructed from a suitably finite monoidal category. In the other direction, deformations of a point in an En-scheme over characteristic zero, such as a variety over the complex numbers, are indexed by framed n-manifolds. Hochschild (co)homology is an instance of this for n=1. This series will dwell on the foundations of this relationship. The talks will be framed by one main result, and a couple formal applications thereof. The main construction is factorization homology with coefficients in higher (enriched) categories. The body of the talks will focus on precise definitions, emphasizing the essential aspects that facilitate the coherent cancellations which support the main result.

DAY 1 - TALK 1 NOT RECORDED