Lecture (webinar) from a special course
of the Chinese-Russian Mathematical Center
«Donaldson Invariants and Hitchin Moduli Space.
Part II. Higgs bundles and related topics»
|Dr. Qiongling Li
Chern Institute of Mathematics, Nankai University
Bio: Qiongling Li got her Ph.D. from Rice University in 2014. She is currently a research fellow at Chern Institute of Mathematics, Nankai University. Her main research fields are Higgs bundles, harmonic maps, and higher Teichmuller theory. Her recent works have been focused on understanding the non-abelian Hodge correspondence over Riemann surfaces.
Higgs bundles over a complex manifold is a natural generalization of holomorphic vector bundles and variation of Hodge structures. The main goal in this short course is to introduce Higgs bundles and associated research topics. Firstly, the non-abelian Hodge correspondence gives a homeomorphism between the representation variety of the surface group into a noncompact Lie group and the moduli space of Higgs bundles. In this way, Higgs bundles plays an important role in the study of higher Teichmuller theory as the generalization of classical Teichmuller theory into higher rank Lie groups. Secondly, the Hitchin fibration on the moduli space of Higgs bundles shows it is a classical integrable system which links with geometric Langlands correspondence.
This short course consists of two parts. In the first part, I will introduce Higgs bundles, moduli spaces, Hitchin integrable system, spectral curve, non-abelian Hodge correspondence, higher Teichmuller theory, etc. I will show some lower rank examples to link Higgs bundles with explicit geometry. In the second part, I will explain current developments on several selected research topics such as Hitchin WKB problem, harmonic maps for Hitchin representations, algebraic structures of the nilpotent cone, and the Hitchin-Kobayashi correspondence over non-compact surfaces.
The lecture will be held in English in the form of a webinar on the Zoom platform.
20:00 - 21:30 Beijing time（15:00 - 16:30 Moscow time)
Join Zoom Meeting:
Meeting ID：862 7775 8883
(link may change closer to the event)
- References for the course “Higgs bundles and related topics” (PDF)
- lecture notes (PDF) from 26.04.2022, 03.05.2022, 10.05.2022