Speaker: Jeroen Sijsling
Date: 10:30 18/09/2020
Title: Arithmetic Fuchsian groups and canonical models
Abstract: This talk will first define Fuchsian groups, their relation with periods, and the notion for a Fuchsian group to be arithmetic,
before proceeding to an important finiteness result by Takeuchi: Given a signature s = (g; e_1, ..., e_N), the number of arithmetic Fuchsian groups
with signature s is finite up to conjugation by PSL_2 (R).
After this, we discuss to the more concrete question of determining all arithmetic Fuchsian groups of signature (1; inf) and (1; e). The solution to
the former admits an ad-hoc approach, whereas the latter (summarized more briefly) can be resolved by the use of methods from arithmetic geometry and
Shimura's theory of canonical models.