Quantum representations of mapping class groups and factorization homology

Abstract: Quantum representations of mapping class groups are finite-dimensional representations of mapping class groups that have their origin in quantum algebra (e.g. the representation theory of Hopf algebras) and that often has strong ties to three-dimensional topological field theory. After explaining the interest in these representations from the perspectives of algebra, topology and mathematical physics and how they can be formally described through modular functors, I will give an idea of the classical construction procedures. I will then present a new and more general construction procedure using cyclic and modular operads, as well as factorization homology. The main result of this approach is a classification of modular functors. This is based on different joint works with Lukas Müller and Adrien Brochier.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home