8 papers
Cleanliness and the Varchenko-Gelfand algebra
Graham Denham, Galen Dorpalen-Barry, Nicholas Proudfoot
A central question in the theory of hyperplane arrangements is when the complement of a complex arrangement is aspherical. Barkley and Speyer introduced a class of real arrangement…
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…
The Ehrhart polynomial of a matroid specializes to the beta invariant
Anastasia Chavez, Galen Dorpalen-Barry, Luis Ferroni +3
We show that the linear coefficient of the Ehrhart polynomial of a matroid base polytope evaluated at is equal to, up to normalization, the -invariant of the matroid. Thi…
Shi arrangements restricted to Weyl cones
Galen Dorpalen-Barry, Christian Stump
We consider the restrictions of Shi arrangements to Weyl cones, their relations to antichains in the root poset, and their intersection posets. For any Weyl cone, we provide biject…
Salvetti complexes for conditional oriented matroids
Galen Dorpalen-Barry, Dan Dugger, Nicholas Proudfoot
We give a new proof of the fact that the complement of the complexification of a real hyperplane arrangement is homotopy equivalent to the Salvetti complex of the associated orient…
The geometry of zonotopal algebras I: cohomology of graphical configuration spaces
Colin Crowley, Galen Dorpalen-Barry, André Henriques +1
Zonotopal algebras of vector arrangements are combinatorially-defined algebras with connections to approximation theory, introduced by Holtz and Ron and independently by Ardila and…