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Polypositroids and membranes

QMAP Seminar

Speaker: Alex Postnikov, MIT
Location: 2112 MSB
Start time: Fri, Dec 8 2017, 1:30PM

Positroids and plabic graphs are certain combinatorial objects that appear in the study of the positive Grassmannian. Interestingly, they also appear in many other areas of mathematics and physics, for example, in the study of scattering amplitudes. We will discuss a generalization of these objects given in terms of convex polytopes, reflection groups and root systems. Polypositroids (which generalize positroids) are convex polytopes with prescribed directions of edges and facet normals given by roots and twisted roots. Membranes (which generalize plabic graphs) are certain 2-dimensional surfaces living inside these polytopes. These objects are closely related to Coxeter elements in reflection groups and decompositions of Coxeter elements. The talk is based on a joint work with Thomas Lam.