Witt group of modular categories (joint work in progress with A. Kitaev, M. Müger, D. Nikshych, V. Ostrik)

We describe an abelian group structure on the set of classes of modular categories modulo some equivalence relation. The resulting Witt group of modular categories resembles (and contains) the Witt group of finite abelian groups with quadratic forms. The conjecture of Moore and Seiberg, that all chiral rational conformal field theories come from reductive groups via WZW, coset and orbifold constructions, can be interpreted as a statement about generators of this Witt group.