This lecture series ‘category theory and its applications’ is linked to the LMS funded Yorshire and Midlands Category Seminar (YaMCATS) network.

This lecture series consists of two topics which illustrate the power of categorical methods to other areas of pure mathematics, mathematical physics and computer science.

The first topic is on the theory of differential categories, to be presented by Jean-Simon Lemay (University of Oxford). The theory of differential categories uses category theory to study the foundations of differentiation. Differential categories have been able to formalize various aspects of differentiation, from the very basic foundational aspects of differentiation to the more complex notions of differential geometry.

The second topic is mapping class groupoids and motion groupoids, to be presented by Fiona Torzewska (University of Leeds).The lectures will explore the use of these categorical structures in the context of topological phase of matter, that is a physical system whose behaviour is effectively described by a topological quantum field theory.