Flawlessness of h-vectors of broken circuit complexes



One of the major open questions in matroid theory asks whether the h-vector (h_0,h_1,...,h_s) of the broken circuit complex of a matroid is weakly increasing in its first half and also satisfies that h_i is at most h_{s-i} whenever i is between zero and s/2. In this talk, we give an affirmative answer to this question for matroids that are representable over a field of characteristic zero.



This is joint work with Din van Le