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.