3 papers
math.GR2025
Categorification of characteristic structures
Peter A. Brooksbank, Heiko Dietrich, Joshua Maglione +2
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing o…
math.GR2025
Smooth cuboids in group theory
Joshua Maglione, Mima Stanojkovski
A smooth cuboid can be identified with a matrix of linear forms, with coefficients in a field , whose determinant describes a smooth cubic in the projective plane. T…
math.CO2024
The Poincaré-extended ab-index
Galen Dorpalen-Barry, Joshua Maglione, Christian Stump
Motivated by a conjecture concerning Igusa local zeta functions for intersection posets of hyperplane arrangements, we introduce and study the Poincaré-extended ab-index, which ge…