Gergen Lectures Seminar
Tuesday, March 1, 2011, 4:30pm, 119 Physics
Andrei Zelevinsky (Northeastern University)
Quivers with potentials, their representation and mutations
Abstract:- A quiver is a finite directed graph. 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 joint work
with H. Derksen and J. Weyman (based on an earlier joint work
with R. Marsh and M. Reineke) we extend these functors to
arbitrary vertices. This construction is based on a framework
of quivers with potentials; their representations are quiver
representations satisfying relations of a special kind between
the linear maps attached to arrows. The motivations for this
work come from several sources: superpotentials in physics,
Calabi-Yau algebras, and cluster algebras. However, no special
knowledge will be assumed in any of these subjects, and the
exposition aims to be accessible to graduate students. [video]
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