Marco De Renzi (Zürich)
Abstract
In recent years, several constructions in the field of quantum topology have been extended to various non-semisimple settings, producing TQFTs with remarkable new properties. At present, all the different approaches rely on a rather elaborate technical setup, involving either the structure of Hopf algebras, or more abstract categorical machinery. In this talk, we will explain how the non-semisimple quantum invariant associated with the small quantum group Ū_q(sl_2) at an odd root of unity q can be reformulated using a diagrammatic model for the representation theory of Ū_q(sl_2) based on the Temperley-Lieb category and the Kauffman bracket polynomial. This is a joint work with C. Blanchet and J. Murakami.