6 papers · 1 filter
Convex Geometry of Building Sets
Spencer Backman, Richard Danner
Building sets were introduced in the study of wonderful compactifications of hyperplane arrangement complements and were later generalized to finite meet-semilattices. Convex geome…
The Gröbner Version of White's Conjecture is False
Spencer Backman, Nathan Cheung, MichaÅ LasoÅ +2
We show that the toric ideal of the Fano matroid polytope does not have a quadratic Gröbner basis. This resolves in the negative a strong version of White's conjecture from matroi…
Line Shellings of Geometric Lattices
Spencer Backman, Galen Dorpalen-Barry, Anastasia Nathanson +2
Inspired by Bruggesser-Mani's line shellings of polytopes, we introduce line shellings for the lattice of flats of a matroid: given a normal complex for a Bergman fan of a matroid…
Simplicial generation of Chow rings of matroids
Spencer Backman, Christopher Eur, Connor Simpson
We introduce a presentation of the Chow ring of a matroid by a new set of generators, called "simplicial generators." These generators are analogous to nef divisors on projective t…
Generalized angle vectors, geometric lattices, and flag-angles
Spencer Backman, Sebastian Manecke, Raman Sanyal
Interior and exterior angle vectors of polytopes capture curvature information at faces of all dimensions and can be seen as metric variants of -vectors. In this context, Gram's…
Higher-Categorical Associahedra
Spencer Backman, Nathaniel Bottman, Daria Poliakova
The second author introduced 2-associahedra as a tool for investigating functoriality properties of Fukaya categories, and he conjectured that they could be realized as face posets…