Spencer Whitehead, Department of Pure Mathematics, University of Waterloo
"3+ε ways to draw the same picture, or, how to earn the ire of a class of first year linear algebra students"
The ADE diagrams were first drawn in their modern presentation by Coxeter in the early 1930s to enumerate certain kaleidoscopes—finite subgroups of orthogonal groups generated by reflections. In the 1940s, ADE diagrams appeared again in Dynkin's classification of finite semisimple Lie algebras. Since the 1970s, many more instances of ADE classifications have been found in fields such as representation theory, algebraic geometry, quiver theory, gauge theory, and various domains of physics.
In this talk I will discuss the history and prevalence of ADE classifications, as well as present a few simple situations in which they arise: root systems, the McKay correspondence, and Gabriel's theorem. Finally, I will show how the ADE diagrams can be used to generate classes of deceptively simple problems in linear algebra.