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UID:20251022T161704EDT-7552bzNFld@132.216.98.100
DTSTAMP:20251022T201704Z
DESCRIPTION:Title: Matroids\, log-concavity\, and expanders\n\nAbstract: Ma
 troids are combinatorial objects that model various types of independence.
  They appear several fields mathematics\, including graph theory\, combina
 torial optimization\, and algebraic geometry. In this talk\, I will introd
 uce the theory of matroids along with the closely related class of polynom
 ials called strongly log-concave polynomials. Strong log-concavity is a fu
 nctional property of a real multivariate polynomial that translates to use
 ful conditions on its coefficients. Discrete probability distributions def
 ined by these coefficients inherit several of these nice properties. I wil
 l discuss the beautiful real and combinatorial geometry underlying these p
 olynomials and describe applications to random walks on the faces of simpl
 icial complexes. Consequences include proofs of Mason's conjecture that th
 e sequence of numbers of independent sets of a matroid is ultra log-concav
 e and the Mihail-Vazirani conjecture that the basis exchange graph of a ma
 troid has expansion at least one. This is based on joint work with Nima An
 ari\, Kuikui Liu\, and Shayan Oveis Gharan.\n\n \n
DTSTART:20200114T203000Z
DTEND:20200114T213000Z
LOCATION:Room 708\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Cynthia Vinzant (North Carolina State University)
URL:/mathstat/channels/event/cynthia-vinzant-north-car
 olina-state-university-304111
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