# Seminar aimed at a general audience by Shinpei Baba (Univ. Heidelberg)

Title: CP^1-structures on surfaces and representations of surface groups into PSL(2, C)

2016.05.09 | Jane Jamshidi

 Date Fri 20 May Time 14:15 — 15:15 Location 1532-116 (Aud. G1)

Abstract:

We consider certain geometric structure (locally homogeneous structure) on a surface, called CP^1-structure. CP^1-structures are related to different areas such as ordinary differential equations, Riemann surfaces, hyperbolic geometry, and representations of surface groups. Indeed the holonomy representation of every CP^1-structure is a homomorphism from the fundamental group of the surface into PSL(2, C). We discuss the relation between the deformation space of CP^1-structures on a surface and the space of such representations. In particular, I explain about a (2pi-)grafting operation, which creates different CP^1-structures having the same holonomy representation.

Note: This seminar is aimed at a general audience of mathematicians.