Xuesen Na (University of Maryland)

Limiting configuration of SU(1,2) Higgs bundles

Abstract: The moduli space of Higgs bundles, or the space of solutions of Hitchin equations has been a focus of intensive studies in algebraic geometry, symplectic geometry and topology. Recently the asymptotics near the ends of the moduli space has been investigated by studying behavior of solutions for (E,t\Phi) as $t\to\infty$ by Mazzeo et al (2014), Mochizuki (2016) and Fredrickson (2018) for some cases of SL(n,C) Higgs bundles.
In this talk I will present a new result of the limiting behavior of solutions SU(1,2) Hitchin equation, as a first step of extending the study to the G-Higgs bundle with G a real rank-one Lie group. The proof relies on construction of approximate solutions by gluing local models on disks to decoupled solutions which converge to limiting configuration after appropriate scaling. A by-product of the study is an explicit description of spectral data of generic SU(1,2) Higgs bundle by Hecke transformations.

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