### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

OCTOBER 24, 2014

**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.

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491