Victor Ostrik, "Witt group of pseudo-unitary modular tensor categories"

I will talk on my joint work with A.Davydov, M.Mueger and D.Nikshych. The classical Witt group of a field K is a quotient of monoid of non-degenerate quadratic forms over K (with direct sum as an operation) by the hyperbolic quadratic forms. In this talk I will describe a generalization of this group where quadratic forms are replaced by pseudo-unitary modular tensor categories. Namely, we consider a monoid formed by equivalence classes of such categories with operation induced by external tensor product. The Witt group is by definition a quotient of this monoid by the relation which says that class of a Drinfeld center is zero. In this talk I will explain basic results about this group (which generalize basic properties of the classical Witt group) and discuss some open questions.