# Magical nilpotents and higher Teichmuller spaces

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

**Speaker(s):**Brian Collier (University of California, Riverside)

**Location:**SLMath: Eisenbud Auditorium

**Tags/Keywords**

holomorphic connections

Higgs bundles

**Primary Mathematics Subject Classification**

**Secondary Mathematics Subject Classification**

#### 16-Collier

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.

#### 16-Collier

H.264 Video | 895_27263_7881_16-Collier.mp4 |

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