# Steven Rayan

## 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".