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

  1. they become involutions in an appropriate sense, and
  2. 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.