Recent Progress on the Moduli Space of Curves (08w5086)

Arriving in Banff, Alberta Sunday, March 16 and departing Friday March 21, 2008


(University of Utah)

(University of British Columbia)

(Colorado State University)

David Ellwood (Clay Mathematics Institute)


Our main goal, as for any successful workshop, is to foster lively interaction
among the participants, leading to original ideas and new directions in research.
As an essential part of this goal, we would like to incorporate a substantial amount of vertical integration in the structure of the workshop.
In simple words, we would like this workshop to constitute at the same time fertile ground for research progress, and a useful educational environment for graduate students interested in the subject area. All too often research conferences are inaccessible to younger mathematicians; we want to avoid this while not compromising the research quality of the workshop. We realize we are walking a fine line here, and now wish to discuss the organizational structure of the conference we envision will achieve the balance necessary for the success of the workshop.

(1) Our choice of topic is instrumental. To avoid the risk of over-ambition and
dispersion of energies, we have chosen to focus on a very specific problem
(the Faber conjectures), which we deem very interesting for multiple reasons: first, it is a beautiful mathematical problem. Second, the approaches
to the problem that we wish to explore are far reaching, and useful for many
other applications besides the Faber conjectures. Third, the methods of
Givental/Lee and Vakil et al. are in a sense very similar in spirit (both mo-
tivated by Gromov-Witten theory and tuned to a combinatorial description
of the moduli space of curves), yet very different in their technical incarnation. Achieving a better communication, interaction and understanding
between the two groups of persons is bound to yield dividends.

(2) We envision the population to be more or less evenly split between "experts" and graduate students. Reaching critical mass for both groups
should allow for a substantial amount of both vertical and horizontal interaction at all levels.

(3) Two distinguished speakers will give a cycle of 5 morning lectures in the
mornings. Some coordination between the distinguished speakers should
allow for the lectures to start very basic, but eventually end up on the
last day or so showing how the two approaches can interweave. We have
in mind Y.P. Lee and Ravi Vakil as our first candidates for distinguished
speakers. We have had preliminary contacts with both of them and they
have expressed interest in this activity.

(4) If possible, each distinguished speaker lecture should be followed by a short
(maybe half hour) "post-mortem" session (discussion, clarification, exercises, possible projects, preparation of questions for the following day for
the distinguished speakers), led by some semi-expert (this could be an advanced student of the speaker, or a post-doc working in the area).

(5) The afternoons should contain more standard research talks by other participants, allowing for the presentation of various current ideas and results
in the field.

(6) If students are interested and willing, towards the beginning of the work-
shop one afternoon could be devoted entirely to capsule talks by graduate
students. This would be both good practice for the students, and an efficient way way to share their research interests with each others and with the