PhD defence: A dendroidal approach to Goodwillie-Weiss manifold calculus

PLEASE NOTE: If a candidate gives a layman's talk, the livestream will start fifteen minutes earlier.

My thesis focused on the study of the spaces of embeddings of manifolds using the tools of algebraic topology. A manifold is a space like a sphere or the euclidean plane, where one is allowed to use the tools of differentiation and integration one learns in an analysis class. As for algebraic topology, this is the part of mathematics which studies manifolds and other more complicated spaces by producing invariants via algebra.

In the case of my thesis, I made use of the language of operads to study the Goodwillie-Weiss tower: this is a sequence of spaces that associates to certain manifolds a family of algebraic invariants, which in some cases give us a full understanding of our original problem.