3. Postdoctoral Program - MSRI

the graduate participants to hear an overview talk about Gromov–Witten invariants in symplectic
geometry by Eleny-Nicoleta Ionel (Stanford University) and a talk on Generating families by Lisa
Traynor (Bryn Mawr). These two lecturers had been thoroughly briefed on the diverse nature of
their audience, and managed to find something fresh to say at a good level for everyone. The first
talk served the graduate students as a summing up, while the second introduced a completely new
(and reasonably elementary) approach to symplectic questions.
Evaluation of the components of the program
The lecturers were chosen for the clarity of their expositions and despite the wildly variable backgrounds
of the students, most students seem to get quite a bit out of the lectures. Their enthusiasm
and interest in the material stayed high throughout the two weeks. There were comments from the
students concerning the tight organization of all the lectures — what was learnt in the first week
being used in the second. Immediately following this workshop was the introductory workshop for
the year long program in symplectic and contact geometry and topology. Several of the students
stayed for this workshop too, and one of them specifically commented that the graduate workshop
had beautifully prepared him for the more advanced workshop.
Many students and several lecturers commented that the afternoon question/problem session and
the break out sessions were highly successful and really added a great deal to the workshop. In
particular, these accommodated the varied background of the participants very well, in that the
more advanced students could work with the less advanced students and all get something from
the interaction. In addition the break out sessions allowed many students to fill in gaps in their
background or really come to grips with some basic examples (for example there were discussions
of bundle theory, Chern classes, group actions,...).
The one hour lectures exposed the students to more of the fundamental ideas in the field than
could have been done in the lecture series alone. We did not hold any of these talks in the first
week as we used the entire afternoon to run the question/problem sessions and break out sessions.
This really helped the students focus on the basic material and prepare them for everything in the
second week.
The capstone meeting was a good way to end the program. It helped sum up what the students
had learned over the previous two weeks, and pointed them towards new ideas and problems.
Students
The students in the program had very diverse backgrounds. An informal servey at the beginning of
the program indicated that approximately 1/3 were beginning graduate students (that is, had been
in graduate school for about 1 or maybe 2 years) and a little less than 1/3 were advanced (that
is within a year or so of graduating). In addition somewhat more than half had some exposure to
symplectic geometry before and somewhat less than 1/3 had exposure to contact geometry.
Having students from across the country was a real strong point of the workshop, but the extremely
varied backgrounds made it a bit difficult for the lecturers to find the level to aim their lectures.
In the future, it might be useful to have the students fill out a survey quite a while before the
workshop. That way the lecturers will know exactly what to expect. It might also be possible
to break the students into various groups (like advanced but no exposure to subject, beginning
student, ...) and send each of the groups an e-mail with suggestions about what they can do to
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