Positive Geometry

A positive geometry of dimension is an oriented real semialgebraic set together with a unique meromorphic differential d-form, called its canonical form, whose only singularities are logarithmic singularities on the boundaries of the set and whose residues are the canonical forms of those boundaries. A closed interval is the one-dimensional prototype. Convex polytopes, positive Grassmannians, and amplituhedra provide higher-dimensional examples.