ICTS:29531

Equivariant Minimal Surfaces in the Symmetric Spaces via Higgs Bundles. (Lecture 3)

APA

(2024). Equivariant Minimal Surfaces in the Symmetric Spaces via Higgs Bundles. (Lecture 3). SciVideos. https://youtube.com/live/70_sj2n1XGY

MLA

Equivariant Minimal Surfaces in the Symmetric Spaces via Higgs Bundles. (Lecture 3). SciVideos, Sep. 04, 2024, https://youtube.com/live/70_sj2n1XGY

BibTex

          @misc{ scivideos_ICTS:29531,
            doi = {},
            url = {https://youtube.com/live/70_sj2n1XGY},
            author = {},
            keywords = {},
            language = {en},
            title = {Equivariant Minimal Surfaces in the Symmetric Spaces via Higgs Bundles. (Lecture 3)},
            publisher = {},
            year = {2024},
            month = {sep},
            note = {ICTS:29531 see, \url{https://scivideos.org/icts-tifr/29531}}
          }
          
John Loftin
Talk numberICTS:29531
Source RepositoryICTS-TIFR

Abstract

I will first consider the geometry of the complex hyperbolic plane and immersed surfaces therein, in particular the cases of Lagrangian and complex surfaces. The complex surfaces are all minimal, but there are many others as well. As it is a symmetric space, the more general case of harmonic maps from a Riemann surface into the complex hyperbolic plane naturally generates holomorphic data of a Higgs bundle. We impose a compactness condition to relate our study of minimal surfaces to Higgs bundles. Let S be a closed Riemann surface of genus at least 2. Consider then harmonic immersions of the universal cover of S into the complex hyperbolic plane which are equivariant with respect to some representation of the fundamental group of S into the group P U(2, 1) of holomorphic isometries of the complex hyperbolic plane. In this case, the nonlinear Hodge correspondence applies and thus there is a (poly-)stable Higgs bundle over S. In the standard case of the group GL(n, C), this consists of a...