Atlantic Graph Theory Seminar: Pjotr Buys (University of Amdsterdam)

About a year ago Jason Brown spoke in our seminar (of the university of Amsterdam) about the two-terminal reliability polynomial and left us with some questions about the closure of the complex zeros of all such polynomials (the zero-locus). In this talk I will define a way to capture, for a certain parameter, whether the set of all two-terminal reliability polynomials behaves chaotically around this parameter or not, i.e. whether this parameter is active or passive. I call the set of all active parameters the activity-locus and I will show that it is equal to the zero-locus. I will use this framework to prove some fun things about the zero-locus. Although I have not yet figured out how to use this to answer any of the open questions posed by Jason, I am hopeful it might be a step in the right direction.