Annual Report 2005 - Fields Institute - University of Toronto

The seventh annual GLGC, which was co-sponsored by
Fields and Perimeter Institutes, and the University of
Waterloo, included nearly 60 participants, mostly mathematicians
but also a few physicists. Ronald Fintushel
delivered a welcoming speech, and what followed were
nine excellent talks that detailed progress on a number of
important problems in geometry and topology.
Research in geometry is fueled in great part by physics, and
this was evident in the talks. For example, Gukov’s talk
used an analogy with string theory to motivate an ongoing
search for an overarching triply-graded homology of knots
that will unify different knot homologies in much the same
way that M-theory unified the different string theories
in physics. Another example of the pervasive influence of
physics in geometry was Stipsicz’s talk, which outlined the
construction of exotic smooth structures on the five-time
blow-up of complex projective plane and the application
of Seiberg-Witten gauge theory in proving exoticness.
Other topics included conformal compactification and
general relativity, contact homology and cusped flow trees,
Gromov-Witten and Donaldson-Thomas invariants, Hamiltonian
dynamics and Floer homology, loop groups and
models for equivariant K-theory and cohomology, Ricci
curvature for metric measure spaces, and Toeplitz operators
and quantization.
On Saturday evening, conference participants were treated
to a banquet dinner in the Black Hole Bistro followed by a
delightful classical music concert performed by the Perimeter
Ensemble and hosted by the inimitable Tom Allen (CBC
Radio). On Sunday afternoon, conference participants were
given a guided tour of the Perimeter Institute. Thanks to
the diligence of Perimeter’s IT staffs, a DVD of the talks can
be ordered from the organizers.
Geometry Conference group
G e n e r a l S c i e n t i f i c A c t i v i t i e s
Speakers:
Michael Anderson (New York at Stony Brook)
Conformal compactification in Riemannian geometry and
general relativity
Kai Behrend (UBC)
Towards an understanding of Donaldson-Thomas invariants
in terms of Euler characteristics
John Etnyre (Pennsylvania)
Cusped flow trees and contact homology
Tatyana Foth (UWO)
Toeplitz operators, automorphic forms, and quantization
Sergei Gukov (Clay Math)
The superpolynomial for knot homologies
Francois Lalonde (Montreal)
Hamiltonian dynamics and a universal Floer homology
John Lott (Michigan)
Ricci curvature for metric-measure spaces
Eckhard Meinrenken (Toronto)
Small models and twisted differentials
Andras Stipsicz (Alfred Renyi Inst. of Math)
Exotic smooth structures on rational surfaces
Workshop on Numerical and Analytic Methods in Fluid
Dynamics
May 5–7, 2005
Held at Carleton University
Organizers: David Amundsen and Lucy Campbell (Carleton)
The study of fluid dynamics has driven the development of
numerous fundamental analytic and numerical methods
of applied mathematics. As the sophistication of physical
models increases and the scope of applications expands,
the impetus for further developments is as great as ever.
This three day workshop, funded by Fields and MITACS,
brought together researchers from both of these essential
sides of applied mathematics. It provided the opportunity
to share in the latest developments, and foster new collaborations
and avenues of research. In total there were over 28
participants including 18 students.
Fields Institute 2005 ANNUAL REPORT 74