Title: 
Moduli spaces of curves of genus 2 and algebraic number fields

Abstract:  
In this talk, I will present the results of my master’s thesis, the aim of which was to use the computer algebra system Magma to create a database of algebraic number fields that can be assigned to non-empty, zero-dimensional moduli spaces of certain genus 2 curves over the rational numbers. The curves studied have the property that they come with a fixed number of pairs of marked points such that the differences of any two of these points all lie in a cyclic subgroup of the respective curve’s Jacobian variety, where they fulfill certain relations. Based on work by Andreas Kühn and Michael Stoll, I will explain how to obtain models for the moduli spaces, how to assign number fields to them, and present a few results regarding the number fields in our database.