Annual Report 2005 - Fields Institute - University of Toronto

There were two additional associated events which were
partially sponsored by the thematic program. The first was
the Great Lakes Geometry Conference (held at Perimeter on
April 30–May 1, 2005 – see the General Scientific Activity
section for a description of this event). In particular, one
plenary talk was given by the well-known string theorist,
Sergei Gukov, from the Clay Mathematics Institute. Many
other talks were related to areas of mathematics allied to
string theory (for example, knot theory, geometric quantization,
symplectic geometry and topology). The second
associated event was a special session at the Canadian
Mathematical Society summer meeting, which was held at
the University of Waterloo (June 4–6, 2005) - see the Joint
Institutes Initiative section for a description. L. Jeffrey, B.
Khesin and R. Myers organized the special session on String
Theory and Integrable Systems. Dan Freed (Texas at Austin)
delivered a lecture on Correspondences, K-theory and loop
groups as the plenary speaker invited in connection with
this Special Session.
There were two graduate courses taught at Fields on physics
topics in the fall term: Mirror Symmetry by Kentaro Hori
and String Theory by Amanda Peet. These were both crosslisted
with the Physics Department at University of Toronto
and were well-attended by students coming from both
Toronto and Waterloo. Two mathematical graduate courses
were taught at Fields in the spring term and cross-listed
with the Department of Mathematics at the University of
Toronto. There courses were Homological Algebra by Ragnar
Buchweitz and Symplectic Geometry and Topology by Boris
Khesin.
Over the year, there were three minicourses: The first,
Frobenius Manifolds, Integrable Hierarchies, was given by
Boris Dubrovin (SISSA, Trieste) at Fields on November 8-
12, 2004. The second minicourse was held at Perimeter over
two weeks on Generalized Geometries in String Theory. In
the week of February 15–17, 2005, Marco Gualtieri (Fields)
gave three lectures on Generalized Geometric Structures
while Yi Li (Caltech) gave three lectures on Twisted Generalized
Calabi-Yau Manifolds and Topological Sigma Models
with Flux. The course concluded in the week of March
1–3, 2005 with three additional lectures by Mariana Grana
(Ecole Polytechnique and Ecole Normale Supérieure) on
Supergravity Backgrounds from Generalized Calabi-Yau
Manifolds. The final minicourse consisted of lectures at
Fields given by B.Khesin, A.Marshakov (on March 31, 2005)
and M.Gekhtman (on May 27, 2005) on Toda lattices: Basics
and Perspectives.
T h e m a t i c P r o g r a m s
The thematic program also included five sets of special
lectures by a superb collection of speakers. These activities
began with the Coxeter lecture series by Nigel Hitchin
(Oxford) on November 15-17, 2004. He lectured on the
geometry of generalized complex manifolds, a topic which
is tied to string theory by the study of B-fields and which
was also seen in the winter minicourse at Perimeter. On
January 17–20, 2005, the Coxeter lecture series was given
by Robbert Dijkgraaf (Amsterdam). He began with a
beautiful general lecture on Mathematics in String Theory
and followed this by two lectures on Topological String
Theory. Next on April 4–7, 2005, the Distinguished Lecture
Series by Edward Witten (IAS, Princeton) dealt with the
mathematical background behind well-known constructs
in theoretical physics (scattering theory and its relation
to analysis; solid state physics and the theory of superconductors,
and its relation to four-manifold geometry
via the Seiberg-Witten equations; and the quantum Hall
effect with its relation to knot invariants). Renata Kallosh
(Stanford) was the final Coxeter lecturer delivering a series
of talks on May 9–11, 2005 describing recent progress on
using string theory to describe early universe cosmology.
All of the above lecture series included lectures delivered at
both the Fields and Perimeter Institutes. The final special
lecture was a Clay Math Institute Public Lecture by Eric
Zaslow entitled Physmatics on June 2, 2005 at Fields – Eric
is a Clay Institute Senior Scholar whose funding from the
Clay Institute supported his participation in the program.
The seminar series was the driving force of the program
and the interaction center of the program participants
throughout the year. The talks and lecture series were
given by program visitors, postdocs and guests of the
University of Toronto Mathematics Department. Parallel
series of seminars were held at both locations, Fields and
Perimeter. The scheduling was arranged to maximize the
interaction of program participants at both locations. In
fall 2004, the regular seminars were held on Mondays at
Fields and on Thursdays at Perimeter. For winter/spring
2005, the schedule was shifted to Tuesdays and Thursdays
at Perimeter and Fields, respectively. In the mathematics
domain, an impressive variety of topics was presented,
ranging from representation and category theories to
decorated Teichmüller spaces and mirror symmetry and
Donaldson-Thomas invariants. A similarly diverse array of
physics topics were discussed in the seminars, ranging from
topological M-theory and holographic cascades for quiver
theories to experimental constraints on supersymmetric
theories coming from the cosmic microwave background.
Overall the seminar series saw a good representation of the
Fields Institute 2005 ANNUAL REPORT 11