Generalized hyperpolygons, meromorphic Higgs bundles on curves, and integrability

Seminar: 
Clusters and Geometry
Event time: 
Friday, December 11, 2020 - 1:00pm
Speaker: 
Steven Rayan
Speaker affiliation: 
University of Saskatchewan
Event description: 

In this talk, I will construct a moduli space of generalized hyperpolygons from a comet-shaped quiver. The resulting Nakajima quiver variety can be interpreted as a distinguished subvariety of a moduli space of meromorphic Higgs bundles on a punctured curve. I will discuss how the moduli space inherits, for complete and minimal flags, a Gelfand-Tsetlin-type integrable system from the reduction of a product of cotangent bundles of (partial) flag varieties. This is joint work with Laura Schaposnik.