This talk will examine two questions:
- Which quivers have only finitely many indecomposable representations? In other words, when can the behavior of a collection of linear maps be summarized by discrete data?
- Consider a collection of hyperplanes in R^n. When do the reflections across these hyperplanes generate a finite group?
The answers to both questions are classified by the Dynkin diagrams, a list of graphs which shows up throughout representation theory, combinatorics, and algebraic geometry. We'll track these two questions back to the source of their commonality and showcase some other hidden connections between them. Speaker(s): Will Dana