5 papers
A construction of polyptych lattices via a pair of Gorenstein PL cones
Laura Escobar, Megumi Harada, Christopher Manon
The theory of polyptych lattices seeks to incorporate, into a single combinatorial framework, the piecewise-linear bijections (mutations) that appear in many theories that generali…
Curves of best approximation on wonderful varieties
Christopher Manon, David McKinnon, Matthew Satriano
We give an unconditional proof of the Coba conjecture for wonderful compactifications of adjoint type for semisimple Lie groups of type . We also give a proof of a slightly we…
Gorenstein-Fano polytopes and compactifications of rank 2 polyptych lattices
Adrian Cook, Laura Escobar, Megumi Harada +1
The theory of polyptych lattices was introduced by Escobar, Harada, and Manon, in an effort to simultaneously generalize combinatorial and geometric phenomena seen in toric, cluste…
Geometric families of degenerations from mutations of polytopes
Laura Escobar, Megumi Harada, Christopher Manon
We introduce the notion of a polyptych lattice, which encodes a collection of lattices related by piecewise linear bijections. We also define and study PL (polyptych-lattice) polyt…
Dissimilarity maps on trees and the representation theory of $GL_n(\C)$
Christopher Manon
We revisit the representation theory in type used previously to establish that the dissimilarity vectors of phylogenetic trees are points on the tropical Grassmannian variety. W…