What is a hyperpolygon?

Abstract: Hyperpolygons are geometric objects originating in representation theory and, in particular, act as a bridge between a number of important geometric and representation-theoretic moduli spaces. Given this role, hyperpolygons interact naturally with a number of other notions that have been presented in this series, including Higgs bundles, character varieties, hyperkähler geometry, nonabelian Hodge theory, integrable systems, mirror symmetry, and Coulomb branches, to name a few. In the first part of the talk, we will review the construction of a Nakajima quiver variety, of which hyperpolygon space is a particular instance. In the second half of the talk, we will focus on the connections that hyperpolygons have with the various other notions from this series, which include a number of recent, interesting results.

algebraic geometrycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: learners

What is ...? Seminar

Series comments: The ``What is ... ? Seminar'' (WiSe) is a weekly Zoom mathematics seminar. The goal is to explain interesting things to each other in a casual manner. The name is inspired by the What is ...? column of the Notices of the American Mathematical Society. See the website for more details. If you want to receive the zoom link for the talks please fill out the form linked on the website or contact Anna at a.puskas@uq.edu.au.