Skip to main content
To KTH's start page To KTH's start page

Lukas Woike: Derived modular functors

Time: Wed 2020-02-26 13.15

Location: KTH, 3418

Participating: Lukas Woike, Hamburg

Export to calendar


I will present a new approach to a class of non-semisimple representation categories, more specifically non-semisimple modular tensor categories, via homotopy theory and low-dimensional topology. This will lead to so-called derived modular functors.

It is already well-known that for a semisimple modular tensor category, the Reshetikhin-Turaev construction yields an extended three-dimensional topological field theory and hence by restriction a modular functor. By work of Lyubachenko-Majid the construction of a modular functor from a modular tensor category remains possible in the non-semisimple case. We explain that the latter construction is the shadow of a derived modular functor featuring homotopy coherent mapping class group actions on chain complex valued conformal blocks and a version of factorization and self-sewing via homotopy coends. On the torus, we find a derived version of the Verlinde algebra, an algebra over the little disk operad. The concepts will be illustrated for modules over the Drinfeld double of a finite group in finite characteristic. This is joint work with Christoph Schweigert (Hamburg).

Belongs to: Stockholm Mathematics Centre
Last changed: Feb 20, 2020