Department of Mathematics
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A quiver is just a (finite) directed graph (possibly with multiple edges). The word "quiver" is used to distinguish the kinds of uses one intends to make of these directed graphs. A representation of a quiver over a field $k$ is an assignment of a $k$ vector space to each vertex of the quiver and a linear map between vector spaces to each arrow.

Quivers arise naturally in describing many problems in combinatorics and algebra. I will discuss the basic representation theory, including indecomposable representations. Then I will describe the path algebra of a quiver and its relationship to representations. I will finish with some important problems in finite dimensional algebras over a field

This talk is based, in part, on Quiver Representations, by Harm Derksen and Jerzy Wyman, which appeared in Notices of the AMS, Vol. 52, No. 2, 200-206, February 2005.