The University of Michigan Combinatorics Seminar
We study the Bergman complex B(M) of a matroid M: a polyhedral
complex which arises in algebraic geometry, but which we describe purely
combinatorially. We prove that a natural subdivision of the Bergman
complex of M is a geometric realization of the order complex of its
lattice of flats. In addition, we show that the Bergman fan B'(K_n) of the
graphical matroid of the complete graph K_n is homeomorphic to the space
of phylogenetic trees T_n.