The Coxeter--Dynkin diagrams of type ADE occur in so many different parts of mathematics, from singularity theory to mathematical physics to graph
theory, that they surely play a very deep role in our subject. In the present
century, they have occurred in the theory of cluster algebras by Fomin and
Zelevinsky, and a constructive version of the McKay correspondence has been found by Dechant. The talk will discuss some of these connections.