Topology and geometry of the moduli space of curves

March 28 to April 1, 2005

at the

American Institute of Mathematics, San Jose, California

organized by

Ulrike Tillmann and Ravi Vakil

Original Announcement

This workshop will be devoted to bringing together the communities of topologists and algebraic geometers. The aim is to have an active exchange of results, techniques and ideas on the cohomology of the moduli spaces of curves.

Recent years have seen major advances in the study of the topology of moduli spaces of Riemann surfaces. Since Mumford initiated the systematic study of the cohomology of moduli spaces some twenty years ago, this has been a major topic of research for many mathematicians with much of the interest motivated by mathematical physics.

Major breakthroughs have been achieved by two different groups, algebraic geometers on the one hand and homotopy theorists on the other, the most significant being the proof of a strong version of Mumford's conjecture by Madsen and Weiss. The workshop intends to promote cross-fertilization between these two camps. Initial lectures will be aimed at introducing each group to the other's results and basic techniques.

Specific topics to be addressed include:

  1. Integral cohomology, stable and unstable.
  2. Tautological cohomology of the compactified moduli space.
  3. Applications to Gromov-Witten theory.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

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.

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.

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