  Let M be a matroid on E, representable over a field of characteristic zero.
We show that h-vectors of the following simplicial complexes are log-concave:
1. The matroid complex of independent subsets of E. 2. The broken circuit
complex of $M$ relative to an ordering of E. The first implies a conjecture of
Colbourn on the reliability polynomial of a graph, and the second implies a
conjecture of Hoggar on the chromatic polynomial of a graph. The proof is based
on the geometric formula for the characteristic polynomial of Denham,
Garrousian, and Schulze.
