The (tree) amplituhedron. We prove this duality using the twist map of Marsh and Scott. We
also show that this map preserves the canonical differential forms associated with the …

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We use inequalities to completely describe the set of boundary correlation matrices of planar
Ising networks embedded in a disk. Specifically, we build on a recent result of Lis to give a …

In this paper, we prove that points in the space Xk; n/of configurations of n points in CPk1
which are fixed under a certain cyclic action are the solutions to the generalized scattering …

The cyclic sieving phenomenon of Reiner, Stanton, and White says that we can often count
the fixed points of elements of a cyclic group acting on a combinatorial set by plugging roots …

In this paper we study the role of planarity in generalized scattering amplitudes, through
several closely interacting structures in combinatorics, algebraic and tropical geometry. The …

We construct the twist automorphism of open Richardson varieties inside the flag variety of a
complex semisimple algebraic group. We show that the twist map preserves totally positive …

We introduce a family of spaces called critical varieties. Each critical variety is a subset of
one of the positroid varieties in the Grassmannian. The combinatorics of positroid varieties is …

We show that the monotone Lagrangian torus fiber of the Gelfand-Cetlin integrable system
on the complex Grassmannian Gr (k, n) supports generators for all maximum modulus …

One can view a partial flag variety in C n as an adjoint orbit O λ inside the Lie algebra of n× n
skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a …