** 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.