Tropical varieties, algebraic cycles, and convexity in combinatorial geometries

The chromatic polynomial of a graph is a polynomial in q which counts the number of colorings of the graph using q colors. Read’s conjecture predicts that the coefficients of the chromatic polynomial form a log-concave sequence. I will outline a proof and explain its relation to a theory of characteristic classes of affine varieties. The analogous conjecture of Rota for possibly non-coordinatizable combinatorial geometries leads us to a question concerning certain tropical varieties. This talk is based on a joint work with Eric Katz.