Bernhard Koeck (University of Southampton)
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.