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Title:
The log-concavity conjecture and the tropical Laplacian
Speaker:
Abstract:
The log-concavity conjecture predicts that the coefficients of the chromatic (characteristic) polynomial of a matroid form a log-concave sequence. The known proof for realizable matroids uses algebraic geometry in an essential way, and the conjecture is open in its full generality. I will give a survey of known results and introduce a stronger conjecture that a certain Laplacian matrix associated to a matroid has exactly one negative eigenvalue. This talk will be followed by talk of Karim Adiprasito at March 3, who recently proved the log-concavity conjecture for a large class of non-realizable matroids.
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