at the
American Institute of Mathematics, San Jose, California
organized by
Ulrike Tillmann and Ravi Vakil
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:
The workshop schedule.
A report on the workshop activities.
Glossary:
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.
Bibliography:
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 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?
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
Please send them to
Jeff Giansiracusa giansira@maths.ox.ac.uk
or Davesh Maulik dmaulik@math.princeton.edu.
