### Mathematics Colloquium

# Andrei Zelevinsky

### (Northeastern University)

## "Quiver representations and their mutations"

** Date: ** |
Wed, April 27, 2011 |

** Time: ** |
17:15 |

** Place: ** |
Research III Lecture Hall |

**Abstract:** A quiver is a finite directed graph, that is, a finite set of vertices
some of which are joined by one or more arrows. A quiver
representation assigns a finite-dimensional vector space to each
vertex, and a linear map between the corresponding spaces to each
arrow. A fundamental role in the theory of quiver representations is
played by Bernstein-Gelfand-Ponomarev reflection functors associated
to every source or sink of a quiver. We will discuss how to modify
these functors so that

- they become involutions in an appropriate sense, and
- they become attached to arbitrary vertices.

The first problem was solved in a joint work with R.Marsh and
M.Reineke, while the second construction was carried out in a joint
work with H. Derksen and J.Weyman.
Motivations for this work come from several sources: superpotentials
in physics, non-commutative geometry, cluster algebras. However no
knowledge is assumed in any of these subjects, and the exposition will
be accessible to graduate students.