Date | May 09, 2024 |
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Speaker | Arnaud Maret |

Dept. | Sorbonne Université |

Room | 27-220 |

Time | 15:30-18:00 |

Time: 7 May 2024 (Tuesday) 15:30 - 18:00 & 9 May 2024 (Thursday) 15:30 - 18:00

Place: 27 (Building) 220 (Room)

Title: Surface group representations - it's not all about Teichmüller!

Abstract: This mini-course is an introduction to surface group representations which are not discrete and faithful. We'll mostly look at representations into PSL(2,R). I'll start with some generalities about surface group representations and character varieties (Goldman symplectic structure, Toledo number, etc). I'll then explain what is known and conjectured about these non-(discrete and faithful) representations. I'll insist on two aspects: mapping class group dynamics and geometrization. We'll finally study a very specific family of such representations: the so-called Deroin-Tholozan representations. They are in some sense the best model of non-(discrete and faithful) representations that we know. Along the way, we'll encounter triangle groups, some elementary algebraic geometry, group cohomology, and much more!

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