Mathematics Colloquium: Enumeration in polytopes and Coxeter groups
Speaker: Lou Billera, Cornell University
Title: Enumeration in polytopes and Coxeter groups
Abstract: There are curious parallels between the enumeration of faces and flags in convex polytopes and the enumeration of chains in a standard partial order - the Bruhat order - on the elements of an arbitrary Coxeter group. Both define so-called Eulerian posets, but this is far from giving the whole story. There are important invariants in each theory, the g-polynomial for polytopes and the Kazhdan-Lusztig polynomial for Bruhat intervals, that are known to have many similar properties. I will outline these theories and their parallels, and offer some speculation on what may be behind the similarities.
I will assume familiarity with neither polytopes nor Coxeter groups.
Time: Friday, October 24, 2014, 3:30-4:20 p.m.
Place: Exploratory Hall, room 4106
Refreshments will be served at 3:00 p.m.