Abstract: By moduli space of Riemann surfaces of genus g, we mean the set of isomorphism classes of complex analytic structures on a closed oriented surface of genus g, fixed once and for all. It is not clear a priori why this definition makes sense, nor whether this set has an extra structure, turning it into a "space". In order to explicitly view the space-like properties of this set, we shall fix g=1 and we also fix some extra data: a base point on the curve. The moduli space we obtain by doing this is called the moduli space of elliptic curves and the goal of the talk is to show that this space is a complex analytic space in a coarse sense, and to introduce the notions of a stack in order to have a finer representation of the classification problem.

(Organiser: Professor Dr. Alexander Schmitt)