Discrete CATS Seminar
####
**
UNIVERSITY OF KENTUCKY **

DISCRETE CATS SEMINAR

AKA

DISCRETE MATH AND COMBINATORICS: ALGEBRAIC & TOPOLOGICAL SEMINAR

113 PATTERSON OFFICE TOWER

FALL 2007

##
"Toric Arrangements"

Richard Ehrenborg

University of Kentucky

###
Monday, September 10, 2007

4:00 pm, 113 Patterson Office Tower

####
Abstract:

In the 1970's Zaslavsky initiated the modern study of hyperplane
arrangements. For a central hyperplane arrangement he showed that
evaluating the characteristic polynomial at -1 gives the number of
regions in the complement of the arrangement. For central arrangements
Bayer and Sturmfels proved its flag f-vector can be determined by the
intersection lattice. Billera, Ehrenborg and Readdy made this map
explicit using coalgebraic techniques.

We extend the Billera-Ehrenborg-Readdy omega map to toric hyperplane
arrangements. We also generalize Zaslavsky's fundamental result on
the number of regions. We believe these results hint at a wealth of
problems involving regular subdivisions of manifolds. I will indicate
a few of these directions.

This is joint work with Margaret Readdy and Michael Slone.