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