The property of inductive factorizability of a hyperplane arrangement, which is one way an arrangement can be shown to be free (definition omitted!), is a matroid property. As such it generalizes to the frame matroid of a gain graph over an arbitrary group. A weaker property is factorizability. I have classified all factorizable gain graphs, which is the first step and probably the biggest step towards a classification of inductively factorizable gain graphs. These properties are technical but are interesting to mathematicians in algebraic and vector geometry as well as matroid theory.
This presentation is Ms. Kaminski's doctoral dissertation defense. All are welcome.
The examining committee members are Laura Anderson, Fernando Guzmán, Hiroaki Terao (outside examiner from Hokkaido University), and Thomas Zaslavsky (chair).