Matroids, log-concavity and measure concentration

Seminar
Speaker
Karim Adiprasito (IHES and Hebrew University)
Date
07/12/2014 - 15:30 - 14:00Add to Calendar 2014-12-07 14:00:00 2014-12-07 15:30:00 Matroids, log-concavity and measure concentration We provide a simple proof of the Rota--Heron--Welsh conjecture for matroids realizable as c-arrangements in the sense of Goresky--MacPherson: we prove that the coefficients of the characteristic polynomial of the associated matroids form log-concave sequences, proving the conjecture for a family of matroids out of reach for all previous methods. To this end, we study the L\'evy--Milman measure concentration phenomenon on natural push-forwards of uniform measures on the Grassmannian to realization spaces of arrangements under a certain extension procedure on matroids. אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Abstract

We provide a simple proof of the Rota--Heron--Welsh conjecture for matroids realizable as c-arrangements in the sense of Goresky--MacPherson: we prove that the coefficients of the characteristic polynomial of the associated matroids form log-concave sequences, proving the conjecture for a family of matroids out of reach for all previous methods.

To this end, we study the L\'evy--Milman measure concentration phenomenon on natural push-forwards of uniform measures on the Grassmannian to realization spaces of arrangements under a certain extension procedure on matroids.

Last Updated Date : 07/12/2014