A classical theorem of Joyal and Street establishes an equivalence between braided categorical groups and quadratic forms.  This  brings an important geometric insight into the theory of braided fusion categories: one can  treat them as non-commutative geometric objects. From this point of view the Drinfeld centers correspond to hyperbolic quadratic forms. We use this observation to define a categorical analogue of the classical Witt group of quadratic forms. It turns out that the categorical Witt group W is no longer a torsion group. We discuss the structure of W and its generalizations: the super and equivariant categorical Witt groups. This talk is based on joint works with Alexei Davydov, Victor Ostrik, and Michael Mueger.

The talk will also be streamed here.



Dmitri Nikshych

Research Area

University of New Hampshire


Wed, 31/05/2017 - 2:00pm to 3:00pm


RC-4082, The Red Centre, UNSW