Joint Colloquium: Nikshych -- The Witt group of braided fusion categories

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.