Rota's conjecture and positivity of algebraic cycles in toric varieties            
-- June Huh, March 7, 2014

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Rota's conjecture predicts that the coefficients of the
characteristic polynomial of a matroid form a log-concave
sequence. I will outline a proof for representable matroids
using the Bergman fan. The same approach to the conjecture in
the general case (for possibly non-realizable matroids) leads
to several intriguing questions on higher codimension algebraic
cycles in the toric variety associated to the permutohedron.