CSM cycles of matroids

I will introduce CSM cycles of an arbitrary matroid M, which are a special collection of balanced polyhedral fans associated to M. In the case the matroid M arises from a complex hyperplane arrangement A, these cycles naturally represent the CSM class of the complement of A. The CSM cycles of M generalize the tropical linear space of M to lower dimensions, and they satisfy very interesting combinatorics. This is joint work with Lucía López de Medrano and Kristin Shaw.