4:00 pm Wednesday, May 6, 2015
Faculty Colloquium: Quiver varieties and representations by Travis Schedler (U.T. Austin) in RLM 5.104
A quiver is another name for a directed graph, coined by Gabriel. A representation of a quiver is an assignment of vector spaces to vertices and linear transformations to edges. Amazingly, from this simple linear algebraic setup Dynkin quivers arise as those with finitely many indecomposable representations. The moduli spaces of quiver representations form interesting varieties with symplectic and quantum analogues including the hyperKaehler ALE spaces and D-modules on flag varieties, and are closely related to semisimple (and Kac-Moody) Lie algebras and quantum groups, wreath product groups, and instanton moduli spaces, as well as to symplectic/mirror duality. They are the subject of a large body of active research and conjectures in algebra, geometry, and physics. I will introduce these varieties and speak about joint work with Gwyn Bellamy in which we classify Nakajima quiver varieties admitting a symplectic resolution of singularities and enumerate the resolutions. Submitted by
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