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.