Characteristic polynomials and the Bergman fan of matroids

June Huh (허준이)

Department of Mathematics, University of Michigan, Ann Arbor, USA

Department of Mathematics, University of Michigan, Ann Arbor, USA

2011/7/28 Thu 4PM-5PM

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.

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