Steven Rayan

(Department of Mathematics, University of Saskatchewan)

Asymptotic geometry of hyperpolygons

Date Thursday, February 1, 2018

Nakajima quiver varieties lie at the interface of geometry and representation theory. I will discuss a particular example, hyperpolygon space, which arises from star-shaped quivers. The simplest of these varieties is a noncompact complex surface admitting the structure of an "instanton", and therefore fits nicely into the Kronheimer--Nakajima classification of ALE hyperkaehler \(4\)-manifolds, which is a geometric realization of the McKay correspondence for finite subgroups of \(SU(2)\). For more general hyperpolygon spaces, we can speculate on how this classification might be extended by studying the geometry of hyperpolygons at "infinity".