Tensor categories, on the one hand, are natural generalizations of Hopf algebras, and on the other hand, they give us a very convenient language both in representation theory and in mathematical physics. For example, many algebraic aspects of two-dimensional conformal field theories can be formulated in the language of tensor categories. I am interested in the problem of deformation of such categories and will talk about new results in this direction. As it is often in algebra, infinitesimal deformations are controlled by Hochschild type complexes. I will show how to use such complexes in rather explicit calculations of deformations of tensor categories and tensor functors arising in Hopf algebra theory.
Peter Schauenburg
