# Manchester Geometry Seminar 2007/2008

**Thursday 8 November 2007. ** *The Frank Adams
Room (Room 1.212), the Alan Turing Building. 4pm*
## Real Bely Theory

Bernhard Koeck (University of Southampton)

`b.koeck@soton.ac.uk`

Belyi's famous theorem states that a compact Riemann surface can be defined over a number field if and only if it admits a meromorphic function with at most three critical values. My talk will be about a generalization of this theorem to Klein surfaces, i.e. (possibly non-orientable) surfaces with boundary which carry a dianalytic structure. I will also explain some other characterizations (triangle groups, maps on surfaces, ...) David Singerman and I have obtained.