Arya Yae: Limiting Configurations in the Moduli of Parabolic Higgs Bundles

Moduli spaces of parabolic Higgs bundles on the four-punctured sphere are examples of ALG gravitational instantons, a kind of complete noncompact hyperkähler 4-manifold with r² volume growth.  There are also ALE, ALF, and ALH instantons with r⁴, r³, and r¹ volume growth respectively.  Gravitational instantons arise as bubbling limits in moduli spaces of K3 surfaces, and degenerations between instantons lends insight into the boundary faces of the compactified K3 moduli spaces.  In this talk, I will discuss a fine-tuned degeneration of the Higgs bundle data which results in the degeneration of the full ALG hyperkähler metric to that of an ALE instanton modeled by a Nakajima quiver variety.  This talk is based on joint work with my advisor Laura Fredrickson.