MIT Combinatorics Seminar
Bergman Complexes, Coxeter Arrangements,
and Graph Associahedra
Lauren Williams (Massachusetts Institute of Technology)
Wednesday, April 6, 2005 4:15 pm Room 2-338
The Bergman complex B(M) and the positive Bergman complex B+(M)
of an oriented matroid M generalize to matroids the notions of
tropical varieties and positive tropical varieties. Our main
result is that if M is the oriented matroid of a Coxeter arrangement, then B(M) equals the nested set complex of that arrangement, and B+(M) is
dual to the corresponding graph associahedron. This recovers
Carr and Devadoss' tiling of the minimal blowup of a Coxeter complex by graph associahedra.
This is joint work with Federico Ardila and Vic Reiner.