Lecture 1 (October 15: 14.30-16.00, Room 0.04) : Moduli and quotients

Abstract: In this lecture we will introduce the concepts of moduli
spaces and quotients in algebraic geometry. No knowledge of algebraic
geometry is required; we shall begin by introducing the necessary basic
definitions. We will then say what is meant by a moduli problem and
relate the solution of such a problem to the construction of quotients
of algebraic varieties by group actions. The second half of the lecture
will be spent discussing examples of quotients.

Lecture 2 (October 18: 14.30-16.00, Room 1.26): Calculation of quotients

Abstract: This lecture is concerned with the construction of quotients
using Mumford's method of geometric invariant theory. We will discuss
affine and projective quotients and the concept of stability.

Lecture 3 (October 19: 14.30-16.00, Room 0.03): Vector bundles on algebraic curves

Abstract: In this lecture we will define vector bundles and describe the
corresponding moduli problem. We will then indicate the solution of this
problem and describe some of the geometric properties of the moduli spaces.