Joseph Chuang, City, University of London

Rank functions on triangulated categories.
A rank function is a nonnegative real-valued, additive, translation-invariant function on the objects of a triangulated category satisfying the triangle inequality on distinguished triangles. One way to obtain a rank function is as the mass of a Bridgeland stability condition, but rank functions may exist in the absence of t-structures. Rank functions on the perfect derived category of a ring are related to Sylvester rank functions on finitely presented modules, and therefore, via the work of Cohn and Schofield, to representations of the ring over skew fields. This is joint work with Andrey Lazarev.