The Bergman complex of a matroid and phylogenetic trees

Federico Ardila


December 3,
refreshments at 3:45pm


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.

The talk will be self-contained and accesible to a general audience.

This is joint work with Carly Klivans.

Speaker's Contact Info: federico(at-sign)

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)

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