Positive Geometry of Polytopes and Polypols
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These are lecture notes supporting a minicourse taught at the Summer School in Total Positivity and Quantum Field Theory at CMSA Harvard in June 2025. We give an introduction to positive geometries and their canonical forms. We present the original definition by Arkani-Hamed, Bai and Lam, and a more recent definition suggested by work of Brown and Dupont. We compute canonical forms of convex polytopes and of quasi-regular polypols, which are nonlinear generalizations of polygons in the plane. The text is a collection of known results. It contains many examples and a list of exercises.
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Forward citations
Cited by 2 Pith papers
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Positive Geometries from Cubic Surfaces
Cubic surfaces are equipped with positive geometries in dimensions 2, 3, and 4 whose positive arrangements, combinatorial ranks, and canonical forms are explored.
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