Title: Nodal domains, spectral minimal partitions, and their relation to Aharonov-Bohm operators,
Abstract: This survey is a short version of a chapter written by the first two authors
in the book [A. Henrot, editor. Shape optimization and spectral theory. Berlin:
De Gruyter, 2017] (where more details and references are given) but we have
decided here to put more emphasis on the role of the Aharonov-Bohm operators
which appear to be a useful tool coming from physics for understanding a
problem motivated either by spectral geometry or dynamics of population.
Similar questions appear also in Bose-Einstein theory. Finally some open
problems which might be of interest are mentioned.