Annual Report 2005 - Fields Institute - University of Toronto

most exciting topics at the cutting edge of research in string
theory.
At Fields, the theme year participants included twelve postdoctoral
fellows in both physics and mathematics: Marco
Gualtieri, Manfred Herbst, Paul Horja, Nan-Kuo Ho,
Shabnam Kadir, Kris Kennaway, Seongchun Kwon, Ruxandra
Moraru, Martin Pinsonnault, Ashish Saxena, Alex
Yong and Ke Zhu. These postdocs were partly supported
by grants from Fields with additional support coming from
the personal NSERC grants of various researchers, as well
as university teaching support. One of these postdoctoral
fellows, Paul Horja, held the Marsden Postdoctoral Fellowship.
Another four (Gualtieri, Ho, Pinsonnault and Yong)
came with NSERC Postdoctoral Fellowships, which may
be taken to indicate both the high quality of the participants
and the external attention drawn to the program. A
substantial number of graduate students participated in
the program, attending the graduate courses and the graduate
Summer School (held at PI). The program sponsored
approximately forty long term visitors, who spent anywhere
from one month to the entire year at Fields and/or Perimeter
as program participants. Activities at Fields were funded
in part by generous sponsorship from Perimeter Institute.
Further funding was also provided by the Connaught Fund
of the University of Toronto, the University of Toronto at
Scarborough and the National Science Foundation.
Of course, the goal of the string program was to stimulate
new science, and also to foster discussions between mathematicians
and physicists on new directions of research.
The full impact of such a program is often difficult to
measure and the new ideas which it stimulates usually do
not come to fruition immediately. However, it is already
clear that this program made a substantial contribution
towards advancing the theory and fostering interaction
between its different domains and researchers with different
backgrounds. There were many positive comments
about the string program from other mathematics and
physics institutions around the world. As an example of the
fruitful interactions, the course and workshop on Mirror
Symmetry catalyzed collaboration of two world-class geometers,
A. Bondal (Steklov Mathematical Institute) coming
from algebraic geometry and W.-D. Ruan (University of
Illinois, Chicago) specializing in symplectic geometry. The
workshop on Topological Strings provided a stage for intensive
discussions between mathematicians and physicists. It
was recognized there, for the first time, that the topological
string partition function should be regarded as the wave
function of some quantum system, both in mathematics
T h e m a t i c P r o g r a m s
and physics. Ragnar Buchweitz’s course on Homological
Algebra catalyzed many discussions around the question of
what is the right mathematical language for string theory.
Even after his course finished, he and many program
participants (including M. Aldi, M. Gaultieri, M. Herbst,
K. Hori, P. Horja, D. Page and several students) continued
in a series of regular meetings to discuss Maximal Cohen-
Macaulay modules and their relation to D-branes in
Calabi-Yau and Landau-Ginzburg models. These meetings
saw a vigorous exchange in which mathematicians and
physicists taught each other what they knew and tried to
learn something they wanted to know. These are just a few
examples of the numerous collaborations and interactions
which were generated by the string program.
Program activities continued beyond the period covered
by this report. The three-week graduate summer school,
Strings, Gravity and Cosmology, took place at Perimeter
Institute. This school brought 23 first-class lecturers and
roughly 90 students from all over the world for lectures
which ran from introductory material to new (as yet unreported)
research results. The final event was Strings 05,
held on July 11-16, 2005 at the University of Toronto. The
“Strings” conferences are the main international meetings
in the field of string theory and they are held annually to
bring together the world’s leading researchers to present
and discuss the latest developments of string theory. Strings
05 marked the first time such meeting was held in Canada!
Both these events will be reported on in detail in next year’s
annual report.
GRADUATE COURSES
Course on Mirror Symmetry
September–December 2004
Instructor: Kentaro Hori (Toronto)
Course on String Theory
September–December 2004
Instructor: Amanda Peet (Toronto)
Mini-Course on Frobenius Manifolds and Integrable
Hierarchies
November 8–12, 2004
Instructor: Boris Dubrovin (SISSA, Trieste)
Course: Introduction to Homological Algebra
January–June 2005
Instructor: Ragnar Buchweitz (Toronto)
Fields Institute 2005 ANNUAL REPORT 12