**ODTÜ-B****İ****LKENT
ALGEBRAIC GEOMETRY SEM****I****NAR**

# “Belyi's
Theorem II”

By

**ALİ SİNAN SERTÖZ**

**(BİLKENT
UNIVERSITY)**

**Abstract: **Last week we discussed the content of Belyi's theorem and worked out an example. So it is only
this week that we start to prove the first part of Belyi's
theorem: If a compact Riemann surface is defined over the field of algebraic numbers,
then it has a meromorphic function which ramifies
over exactly three points. This is know as the hard
part, and the converse is known as the easy part even though the converse is
more involved!

** **

** **

** **

** **

**Date: ****Friday, December 19, 2014**

**Time: ****15.40**

**Place: ****Mathematics Seminar Room,
SA 141**

Tea and cookies will be served before the
seminar.