Geometry/Topology Seminar
Xuesen Na
University of Illinois at Urbana Champaign
Limiting configurations for Hitchin's equation of SU(1,2)-Higgs bundles
Abstract: In this talk, I will begin by giving an accessible overview of Hitchin's self-duality equation and the rich geometry of the space of its solutions -- the Hitchin moduli space. Inspired by a conjectural picture of its asymptotic geometry, the work of Mazzeo-Swoboda-Weiss-Witt (2014) studied the family of solutions with diverging Higgs fields and introduced the notion of limiting configuration.
I will then present a recent progress on limiting configuration for the SU(1,2)-Higgs bundle. The work combines the gluing construction of Mazzeo-Swoboda-Weiss-Witt and the asymptotic estimates of Mochizuki (2016). An explicit description of the spectral data for an SU(1,2)-Higgs bundle plays a key role in the construction of limiting configurations.
If you would like to join the speaker for lunch, please reach out to Nicole at nrlooper@uic.edu
Wednesday September 6, 2023 at 3:00 PM in 636 SEO