Home /  GT Program Seminar: Limiting configuration, spectral data and the SU(1,2) Higgs bundle

Seminar

GT Program Seminar: Limiting configuration, spectral data and the SU(1,2) Higgs bundle September 27, 2022 (11:00 AM PDT - 12:00 PM PDT)
Parent Program:
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Speaker(s) Xuesen Na (University of Illinois at Urbana-Champaign)
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Keywords and Mathematics Subject Classification (MSC)
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Video

GT Program Seminar: Limiting Configuration, Spectral Data And The SU(1,2) Higgs Bundle
Abstract/Media

To participate in this seminar, please register HERE.

In this talk, we will review Hitchin's self-duality equation and Hitchin fibration in the moduli space of Higgs bundles and the notion of limiting configuration. This is in some sense the limiting of a family of hermitian metrics with diverging Higgs field, which has application in the study of asymptotic geometry of the Hitchin moduli space.

We will review the gluing technique of Mazzeo, Swoboda, Weiss, Witt on limiting configuration of SL(2,C) Higgs bundles and discuss a new result for real Lie group SU(1,2). One of the main challenges is dealing with complications of considering singular Hitchin fiber and we will also mention an explicit description of spectral data for the SU(1,2) Higgs bundles.

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GT Program Seminar: Limiting Configuration, Spectral Data And The SU(1,2) Higgs Bundle