ICTS:32620

Minimal surfaces with and without Higgs bundles-I

(2025). Minimal surfaces with and without Higgs bundles-I. SciVideos. https://scivideos.org/index.php/icts-tifr/32620

Minimal surfaces with and without Higgs bundles-I. SciVideos, Aug. 21, 2025, https://scivideos.org/index.php/icts-tifr/32620 

          @misc{ scivideos_ICTS:32620,
            doi = {},
            url = {https://scivideos.org/index.php/icts-tifr/32620},
            author = {},
            keywords = {},
            language = {en},
            title = {Minimal surfaces with and without Higgs bundles-I},
            publisher = {},
            year = {2025},
            month = {aug},
            note = {ICTS:32620 see, \url{https://scivideos.org/index.php/icts-tifr/32620}}
          }
Charles Ouyang
Talk numberICTS:32620
Source RepositoryICTS-TIFR

Abstract

Harmonic maps to symmetric spaces are used in the non-Abelian Hodge correspondence to bridge surface group representations with Higgs bundles. In special cases, these harmonic maps are conformal and hence give minimal surfaces in a symmetric space. In the first lecture, we look at the case of SL(3,R) and describe some asymptotics via Blaschke metrics.

In the second lecture, we will look at higher genus minimal Lagrangians in CP^2. There will be objects reminiscent of Higgs bundles, but which are not Higgs bundles. This will involve loop group methods and satisfying a closing condition.