From modular tensor categories to modular functors

This is the third part of the talks of October 6 and 27. I will introduce the notion of modular functor, and explain how a
modular functor can be obtained from a modular tensor category (Turaev), as well as a partial converse (Bakalov-Kirillov).
In particular, we shall see how representation of central extensions of the mapping class groups occur from modular tensor
categories.