Geometry Seminar

In this talk, I will begin by recalling how the monodromy data of a conformal field theory can be described via representations of mapping class groups. The latter form what is called a modular functor, at least in good cases, most notably for rational conformal field theories. Beyond the rational case, various difficulties arise, not only for the construction of spaces of conformal blocks, but also for the construction of correlation functions. I will explain how factorization homology resolves at least some of these difficulties. In particular, I will give a construction of correlators for finite rigid, but not necessarily semisimple conformal field theories using a generalization of the holographic principle of Fuchs-Runkel-Schweigert. This talk is partially based on work with A. Brochier, C. Damiolini and L. Müller.