Topology and geometry of the moduli space of curves

March 28 to April 1, 2005

at the

American Institute of Mathematics, Palo Alto, California

organized by

Ulrike Tillmann and Ravi Vakil

This workshop, sponsored by AIM and the NSF, will be devoted to bringing the communities of topologists and algebraic geometers together. 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.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and working sessions.

Invited participants include C.-F. Boedigheimer, C. Faber, G. Farkas, E. Getzler, V. Godin, J. Harris, K. Igusa, N. Ivanov, M. Kapranov, S. Keel, M. Kontsevich, Y.-P. Lee, E. Looijenga, I. Madsen, Y. Manin, G. Mikhalkin, M. Mirzakhani, J. Morava, S. Morita, D. Sullivan, C. Teleman, U. Tillmann, R. Vakil, and N. Wahl.

The deadline to apply for support to participate in this workshop has passed.

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