Atlanta, GA | Posted: May 26, 1999
Richard Peter Stanley is the Norman Levinson Professor of Applied Mathematics at the Massachusetts Institute of Technology. He received his Ph.D. at Harvard University in 1971 under the supervision of Gian-Carlo Rota. He is a leading expert in the field of combinatorics and its applications to a variety of other mathematical disciplines. He is the author of the two-volume treatise "Enumerative Combinatorics", the book Combinatorics and Commutative Algebra, and well over 100 research articles in mathematics. Stanley is a member of the National Academy of Sciences and recipient of the 2001 Leroy P. Steele Prize for mathematical exposition.
By a hyperplane arrangement A, we mean a finite collection of affine hyperplanes in Rn. The characteristic polynomial c(A,q) is a polynomial in q of degree n that is a fundamental combinatorial invariant of A. We will survey some connections between c(A,q) and the combinatorial, topological, and algebraic properties of A. A number examples will be presented, including in particular the braid and Linial arrangements.
This will be a survey talk devoted to exact formulas for volumes and lattice point enumerators of interesting classes of convex polytopes. Examples will include the polytope of degree sequences, the Catalanotope, flow polytopes, and the parking function polytope.