ICTS:32610

Harmonic maps and framed PSL(2,C)-representations

(2025). Harmonic maps and framed PSL(2,C)-representations. SciVideos. https://scivideos.org/index.php/icts-tifr/32610

Harmonic maps and framed PSL(2,C)-representations. SciVideos, Aug. 25, 2025, https://scivideos.org/index.php/icts-tifr/32610 

          @misc{ scivideos_ICTS:32610,
            doi = {},
            url = {https://scivideos.org/index.php/icts-tifr/32610},
            author = {},
            keywords = {},
            language = {en},
            title = {Harmonic maps and framed PSL(2,C)-representations},
            publisher = {},
            year = {2025},
            month = {aug},
            note = {ICTS:32610 see, \url{https://scivideos.org/index.php/icts-tifr/32610}}
          }
Subhojoy Gupta
Talk numberICTS:32610
Source RepositoryICTS-TIFR

Abstract

For a closed Riemann surface X, and an irreducible representation R from the fundamental group of X to PSL(2,C), a seminal theorem of Donaldson proves the existence of an R-equivariant harmonic map from the universal cover of X into hyperbolic 3-space. We shall discuss a generalization of this result to the case when X is a punctured Riemann surface arising from an element of the enhanced Teichmüller space, and R is a framed PSL(2,C)-representation. Our technique involves the harmonic map heat flow, and the relation between the asymptotic behaviour of a harmonic map and the singular-flat geometry of its Hopf differential. This is joint work with Gobinda Sau.