June Huh (허준이), Characteristic polynomials and the Bergman fan of matroids

Let V be a subvariety of the complex projective space. The amoeba of V is the set of all real vectors log|x| where x runs over all points of V in the complex torus. The asymptotic behavior of the amoeba is given by a polyhedral fan called the Bergman fan of V. We use the tropical geometry of the Bergman fan to prove the log-concavity conjecture of Rota and Welsh over any field. This work is joint with Eric Katz and is based on arXiv:1104.2519.