### Remarkable surface group representations in genus zero

Geometry and Topology Seminar

19th October 2021, 2:00 pm – 3:00 pm

Online seminar, Please email the organisers to get a zoom link

This talk is about a very special kind of representations of the fundamental group of a punctured sphere into PSL(2,R), discovered by Deroin and Tholozan. We will talk about the topology of their moduli space which turns out to be compact. I will explain how to parametrize them with chains of triangles in the upper half-plane and how to extract action-angle coordinates from that polygonal model. These representations can be geometrized by a certain family of hyperbolic metrics with conical singularities on the punctured sphere.

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