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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.