The University of Michigan Combinatorics Seminar
Winter 2004
April 9, 4:10-5:00, 3866 East Hall

The Bergman complex of a matroid and phylogenetic trees

Caroline Klivans

Cornell University


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.

This is joint work with Federico Ardila.