Bram Petri

Introduction to moduli spaces of Riemann surfaces

Practical information

Dates: 5 January - 13 February 2025

Times and rooms:
- Mondays 8:30 - 10:30 in 15-16-102: Lecture
- Tuesdays 8:50 - 10:50 in 15-16-101: Lecture
- Fridays 8:30 - 10:30 in 15-16-101: Exercises

Contents

Riemann surfaces are objects that appear everywhere in mathematics. Of course, they play an important role in complex analysis and in geometry but also for example in dynamics, number theory and combinatorics.

Their moduli spaces - the spaces that parameterize Riemann surface structures on a fixed surface - are also studied from many different points of view. The goal of this course is to understand the geometry and topology of these moduli spaces.

Lecture notes

I will post notes here. They will be updated after each lecture.
DISCLAIMER: I do not guarantee in any way that these notes are correct. I will be happy to hear of any mistakes that are found.

Lecture notes
Latest update: January 3 2026

Exercises

Problem set 1
Solutions

Problem set 2
Solutions