## JOINT MATHEMATICS COLLOQUIUM

 Quiver representations: basic facts and some recent developments

# Ralf Schiffler

University of Massachusetts, Amherst

### Brandeis University

#### Tea at 4:00 p.m. in 300 Goldsmith Hall

 Abstract:Let $Q = (Q_0,Q_1)$ be a quiver with vertices $Q_0$ and arrows $Q_1$. A representation of $Q$ is a family of vector spaces $(V_i)_{i \in Q_0}$ and linear maps $(f_{ij}) _{i\rightarrow j \in Q_1}$ between the vector spaces. In this talk, we will consider the category of representations of the quiver, or, equivalently, the module category of its path algebra. Then, we will illustrate the links between quiver representations and two other mathematical concepts; quantum groups and cluster algebras.

 Web page: Alexandru I. Suciu Posted: October 17, 2005 Comments to: a.suciu@neu.edu URL: http://www.math.neu.edu/bhmn/schiffler05.html