Some directions in the research in Surface Theory ask for a more explicit approach
to the Uniformization Theorem. Really explicit examples are rare.
In this talk I will therefore focus not on the proof by Koebe based on quasi-conformal
maps, but on Poincaré’s original approach. The key elements in this approach are
projective structures, the Schwarzian derivative, and accessory parameters. At this
the Schottky uniformization and the work of Zograf and Takhtajan on Conformal Field
Theory and later work of McMullen relating all this quasi-Fuchsian uniformization come
into play
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/3050