Student Combinatorics Seminar

One of the key ideas of linear algebra is that we can put matrices in some sort of nice canonical form by carefully choosing bases for the vector spaces involved. The theory of quiver representations addresses the more general question of when this is possible for multiple matrices at once. The answer to this question turns out to rely on a remarkable connection to groups generated by reflections, through the common thread of Dynkin diagrams.

In this talk, I'll give a sketchy introduction to two results highlighting this connection: the foundational 1972 result of Gabriel, and a 2012 result of Amiot-Iyama-Reiten-Todorov which goes deeper on both sides of the connection.

This talk does not assume knowledge of what quiver representations or Coxeter groups are. Speaker(s): Will Dana