collaborators

5 papers

math.CO2025

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…

math.CO2025

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…

math.AG2025

Intersection cohomology of Popov-Vinberg varieties

Andrew Dancer, Johan Martens, Nicholas Proudfoot

The Popov-Vinberg variety of a simply connected, split, semisimple algebraic group is a singular affine variety that contains the basic affine space as a Zariski open sub…

math.AG2025

The geometry of zonotopal algebras II: Orlik--Terao algebras and Schubert varieties

Colin Crowley, Nicholas Proudfoot

Zonotopal algebras, introduced by Postnikov--Shapiro--Shapiro, Ardila--Postnikov, and Holtz--Ron, show up in many different contexts, including approximation theory, representation…

math.CO2025

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…