Algebra and Combinatorics Seminar
The current seminar's organizers are
ChunHung Liu and
Catherine Yan.

Date Time 
Location  Speaker 
Title – click for abstract 

08/26 3:00pm 
BLOC 302 
Galen DorpalenBarry RuhrUniversität Bochum 
Real Hyperplane Arrangements and the VarchenkoGelfand Ring
For a real hyperplane arrangement A, VarchenkoGelfand ring is the ring
of functions from the chambers of A to the integers with pointwise
addition and multiplication. Varchenko and Gelfand gave a simple
presentation for this ring, along with a filtration whose associated
graded ring has its Hilbert function given by the coefficients of the
Poincaré polynomial. Their work was extended to oriented matroids by
Gelfand—Rybnikov, who gave an analogous presentation and filtration.
We extend this work first to pairs (A,K) consisting of an arrangement A
in a real vector space and open convex set K, and then to conditional
oriented matroids. Time permitting, we will discuss an interesting
special case arising in Coxeter theory: Weyl cones of Shi arrangements.
We find that the coefficients of the cone Poincaré polynomial of a Weyl
cone are described by antichains in the root poset.
This talk contains joint work with Christian Stump, Nicholas Proudfoot,
and Jayden Wang. 