Moduli of Riemann Surfaces, Transcendental Aspects

TL;DR

This paper provides an informal overview of moduli spaces of Riemann surfaces, covering elementary cases, Teichmüller space, and higher genus moduli spaces from topological and analytical perspectives.

Contribution

It offers an accessible, lecture-based introduction to the theory of moduli spaces of curves, emphasizing the genus 1 case and the structure of Teichmüller space.

Findings

Detailed discussion of genus 1 moduli space

Informal treatment of Teichmüller space

Topological and analytical perspectives on moduli spaces

Abstract

This is an informal set of lecture notes on moduli spaces of curves based on a set of lectures given at the ICTP last summer. It begins at an elementary level and discusses the genus 1 case in detail. The notes then give an informal treatement of Teichmuller space and higher genus moduli spaces. The point of view is generally topological and analytical.