  Similarities between quantum systems and analogous systems for classical
waves have been used to great effect in the physics community, be it to gain an
intuition for quantum systems or to anticipate novel phenomena in classical
waves. This proceeding reviews recent advances in putting these quantum-wave
analogies on a mathematically rigorous foundation for classical
electromagnetism. Not only has this Schr\"odinger formalism of electromagnetism
led to new, interesting mathematical problems for so-called Maxwell-type
operators, it has also improved the understanding of the physics of topological
phenomena in electromagnetic media. For example, it enabled us to classify
electromagnetic media by their material symmetries, and explained why
"fermionic time-reversal symmetries" --- that were conjectured to exist in the
physics literature --- are in fact forbidden.
