The first part of the talk will give a popular overview of the spectral theory of partial differential operators, charting its development from the non-rigorous work of physicists to the eventual rigorous proof of the Weyl Conjecture.
The second part of the talk will focus on recent progress in the spectral theory of first order systems. These new results motivate us to revisit the fundamental question: why do all the main equations of theoretical physics contain the same physical constant - the speed of light?