The McKay Correspondence

Abstract: 

The simply laced Dynkin diagrams, i.e. those of type ADE, have a habit of showing up in all sorts of places. In this talk, I will discuss how they are related to finite subgroups of SL(2,C) this is also known as the McKay correspondence. I will then go on to describe aspects of the geometry related to the McKay correspondence and some of its generalisations. This will mainly be a survey of the topic and will not assume any previous knowledge of algebraic geometry or representation theory.