COLLOQUIUM
DEPARTMENT OF MATHEMATICS AND STATISTICS
OAKLAND UNIVERSITY
ROCHESTER, MICHIGAN 48309
Andrei Zelevinsky
Northeastern University
Quivers with potentials: representations and their mutations
Abstract
A quiver is a finite directed graph, that is, a finite set of vertices some of which are joined by 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. In a joint work with Harm Derksen and Jerzy Weyman we extend these functors to arbitrary vertices. This is done for quiver representations satisfying relations of a special kind coming from the theory of quivers with potentials. The motivations for this work come from several sources: superpotentials in physics, Calabi-Yau algebras, cluster algebras. However no special knowledge will be assumed in any of these subjects, and the exposition aims to be accessible to graduate students.
Tuesday, March 27, 2012
3:00– 4:00 P.M.
372 Science and Engineering Building
(Refreshments at 2:30-3:00 PM in the kitchen area adjacent to 368 SEB)