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DESCRIPTION: Polypositroids is a class of convex polytopes defined to be th
ose polytopes that are simultaneously generalized permutohedra (or polymatr
oids) and alcoved polytopes. Whereas positroids are the matroids arising fr
om the totally nonnegative Grassmannian\,polypositroids are "positive" poly
matroids. We parametrize polypositroids using Coxeter necklaces and balance
d graphs\, and describe the cone of polypositroids by extremal rays and fac
et inequalities. We generalize polypositroids to an arbitrary finite Weyl g
roup W\, and connect them to cluster algebras and to generalized associahed
ra. We also discuss membranes\, which are certain triangulated surfaces. Th
ey extend the notion of plabic graphs from positroids to polypositroids. Th
e talk is based on a joint work with Thomas Lam.
DTSTAMP:20210608T175900
DTSTART:20210614T163000
CLASS:PUBLIC
LOCATION:online
SEQUENCE:0
SUMMARY:Alex Postnikov (MIT): Polypositroids
UID:107918271@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20210614-L-Postnikov.html
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