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Completely log concave polynomials and Mason’s log concavity conjecture

Shayan Oveis Gharan, University of Washington
Wednesday, November 14, 2018 - 3:40pm
PDL C-401
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We prove the strongest version of Mason’s conjecture, that for any matroid the sequence of the number of independent sets of given sizes is ultra log-concave. To do this, we introduce a class of polynomials, called completely log-concave polynomials (CLC), whose bivariate restrictions have ultra log-concave coefficients.

I will talk about a number of polynomials which are CLC including homogenization of the generating polynomial of independent sets of a given matroid, or the multivariate Tuttle polynomial in certain regimes. If time permits I will talk about connections to High dimensional simplicial complexes.

Based on joint works with Nima Anari, Kuikui Liu and Cynthia Vinzant.

Note: Pre-seminar will start at 3:40pm. The main talk will start as usual at 4:10pm.

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