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