Speaker: Matthew Dyer, University of Notre Dame

Title: Poincaré series of Coxeter groups and multichains in Eulerian posets

Abstract: We describe an analogy between the reciprocals of Poincaré (growth) series of finite rank Coxeter groups with respect to their Coxeter generators, and the fine Hilbert series of face rings of order complexes of lower Eulerian posets, giving in each setting analogues of well known formulae from the other setting. In fact, the reciprocal of the Poincaré series of a Coxeter group is a natural specialization of the fine Hilbert series of the face ring of the barycentric subdivision of the associated nerve, an easily proved observation for which a conceptual explanation is lacking.