On the nodal distribution of quantum graphs

I will give a brief introduction to quantum graphs and the nodal count sequence. I will then present the known bounds on the nodal count and define the nodal surplus. Following these I will state a theorem connecting the nodal surplus to the stability of energy levels under magnetic perturbations, and I will present our theorem regarding the statistics of the nodal surplus and its topological dependence.

This talk is based on the paper:

Alon, L., Band, R. & Berkolaiko, G. Commun. Math. Phys. (2018). https://doi.org/10.1007/s00220-018-3111-2