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Bergman Complex of a Matroid

Algebra & Discrete Mathematics

Speaker: Carly Klivans, MSRI
Location: 693 Kerr
Start time: Fri, Oct 31 2003, 2:10PM

The Bergman complex was first defined as the logarithmic limit set of an algebraic variety. More recently, it has appeared in the thoery of tropical geometry. In a special case, the complex can be reformulated in terms of matroids. We show that the Bergman complex of a matroid is the order complex of the lattice of flats of the matroid. Moreover, we show that for graphical matroids of complete graphs, the Bergman complex is the space of phylogentic trees.