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[theory-seminar] Theory Lunch -- Nima Anari

Reyna Marie Hulett rmhulett at
Tue Oct 9 13:07:43 PDT 2018

Hi everyone,

This week's theory lunch will be given by Nima Anari, on “Log-Concave Polynomials: Combinatorics and Algorithms”--see abstract below. As always, please join us Thursday from noon to 1 pm in Gates 463A!

I will discuss an analytic property of multivariate polynomials, which we call complete log-concavity, and its surprising uses to attack several problems in combinatorics, discrete optimization, and discrete sampling. This property defines a large class of discrete distributions that should be thought of as the analog of the well-studied continuous log-concave distributions. This class includes uniform distributions over bases or independent sets of matroids, determinantal point processes, the random cluster model for some regimes of parameters, and several other generalizations.

I will then discuss an application of this theory in which we resolve a combinatorial conjecture of Mason on the ultra-log-concavity of the number of independent sets of varying sizes in matroids.

Based on joint work with Kuikui Liu, Shayan Oveis Gharan, and Cynthia Vinzant.


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