I give an overview of a host of seemingly unrelated classification problems in mathematics which turn out to be intimately connected through some deep Correspondences.
Some of these relations were uncovered by focusing on so-called exceptional structures which abound: in geometry, there are the Platonic solids; in algebra, there are the exceptional Lie algebras; in group theory, there are the sporadic groups, to name but a few. A champion for such Correspondences is Prof. John McKay.
I also present how these correspondences have subsequently been harnessed by theoretical physicists. My goal is to take a casual promenade in this land of ‘exceptionology’, reviewing some classic results and presenting some new ones based on joint work with Prof. McKay.
Philosophy of Physics Seminar Convenors for HT19: James Read and Simon Saunders