Speaker: Jose Bastidas, Cornell University
Title: The face algebra of a hyperplane arrangement
Time: 2:30 PM, Monday, October 22, 2018
Place: Malott 206
Abstract: In his work on buildings of Coxeter type, Tits introduced the projection operation between faces of the Coxeter complex. This operation can be generalized to the faces of any hyperplane arrangement, inducing an algebra structure on the vector space generated by the faces of the arrangement. This structure has been used to study random walks on the set of chambers of a hyperplane arrangement, and is closely related to the relation between the braid arrangement and Hopf monoids in the category of Species.
In this talk, we will go over the definition of the face algebra and introduce some special elements, which we call characteristic. These encode interesting combinatorial invariants of classical objects such as graphs, partial orders and generalized permutohedra. We construct an interesting family of such elements using intrinsic volumes and recover a result of Klivans and Swartz. Time permitting, we will explain how characteristic elements help generalize a theorem by Stanley on exponential sequences arrangements.