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Magical nilpotents and higher Teichmuller spaces

Introductory Workshop: Holomorphic Differentials in Mathematics and Physics August 19, 2019 - August 23, 2019

August 23, 2019 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Brian Collier (University of California, Riverside)
Location: MSRI: Simons Auditorium
  • holomorphic connections

  • Higgs bundles

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification



In this talk, we will present a special class of nilpotent elements of a complex semisimple Lie algebra. For such a nilpotent element, we will describe how Higgs bundles can be used to construct components of the character variety of a closed surface of genus at least 2. Moreover, such components are deformation spaces of Teichmuller space. The classification of this class of nilpotent elements turns out to be equivalent to Guichard, and Wienhard's notion of Theta-positivity, and so, this construction should describe all Higher Teichmuller spaces. 

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H.264 Video 895_27263_7881_16-Collier.mp4
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