15 citations · 51 across the 20 of their papers we have counts for
26 papers
A Polytopal Realization of Higher-Categorical Associahedra
Spencer Backman, Nathaniel Bottman, Daria Poliakova
We describe a polytopal realization of categorical -associahedra. The normal fan of this polytopal realization is a modification of the authors' velocity fan and was found by Op…
Polytopal bases for barycentric subdivisions
Spencer Backman, Federico Castillo
Several important fans studied at the interface of combinatorics and algebraic geometry arise from barycentric subdivisions of other fans; the central example is the braid arrangem…
The Gröbner Version of White's Conjecture is False
Spencer Backman, Nathan Cheung, Michał Lasoń +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 matroid…
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…
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…
Ford Spheres in the Clifford-Bianchi Setting
Spencer Backman, Taylor Dupuy, Anton Hilado +1
We define Ford Spheres in hyperbolic -space associated to Clifford-Bianchi groups for orders in rational Clifford algebras associated to positive de…