Topology and geometry of the moduli space of curves

This web page is meant to be a collection of resources for mathematicians interested in the moduli space of curves, and related subjects. The content grew out of the ARCC workshop: Topology and Geometry of the Moduli Space of Curves, March 28 to April 1, 2005, organized by Ulrike Tillmann and Ravi Vakil. The workshop was sponsored by AIM and the NSF. The initial announcement is here.

A list of participants is available.


A glossary of terms is available here. Also in pdf format.

This document provides brief definitions of technical terms related to the study of the moduli space of curves. It should be helpful for researchers entering the field and in bridging the communication gap between the different camps studying studying the subject.

Canonical references

An annotated bibliography of canonical references in the subject is available here. Also in pdf format. This should also be an aid to students and to those who wish to learn a different camp's approach to the moduli space of curves.

Open questions

Towards the end of the workshop there was discussion session in which participants generated a list of interesting questions and open problems. Also in pdf format.

Lecture notes

The slides from Kiyoshi Igusa's talk are here in pdf and the original tex.

Scanned images of notes from the talks of Mike Hopkins, Kevin Costello, and Constantin Teleman are available.

Hopkins: 1, 2, 3, 4, 5
Costello: 1, 2
Teleman: 1, 2, 3, 4, 5

The Hopkins-Costello talks were heavily based on material in Costello's paper Topological conformal field theories and Calabi-Yau categories (math.QA/0412149), and a draft of a second paper, Extending topological conformal field theories to Deligne-Mumford space available on Costello's homepage.

Comments, suggestions, corrections, updates? Please send them to Jeff Giansiracusa or Davesh Maulik,