Mathematics Colloquia and Seminars

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Matroids are found in many different combinatorial and geometric structures, such as graphs, point sets, vector spaces, arrangement of hyperplanes and arrangement of pseudospheres. In the first half of the talk I will present basic matroid definitions and examples. In the second half of the talk, I will describe two opens problems in matroid theory. The first is a unimodality conjecture of the h^*-vector, which is derived from the matroid polytope and its Ehrhart series. The second problem deals with algorithmic investigations of matroid polytope decompositions.