




Differential Geometry / Géométrie différentielle (J. Chen, Organizer)
 C. AREZZO, Università di Parma
To be announced

 J. BRYAN, University of British Columbia, Vancouver
GromovWitten theory of local CalabiYau's and TQFT

We study the local GromovWitten theory of a curve in a CalabiYau
3fold. We show this theory can be exhibited as a 1+1 dimensional
topological quantum field theory. This theory is semisimple and leads
to nice closed formulas for the local GromovWitten invariants.
 MIHAIL COCOS, University of British Columbia
On the heatequation method of M. Gaffney

The study of L^{2} harmonic forms on a complete Riemanian manifold is a
very interesting and important subject. It has also found numerous
applications in the field of Mathematical Physics and other related
areas of Mathematics. As early as 1956 M. Gaffney in his PhD thesis at
the University of Chicago proved that the Heat Equation for forms of
arbitrary degree has solution for all time t > 0 and the solution is
smooth (similar results were also obtained by F. Browder). He also
showed that the ``heat flow'' generated by solving this equation
preserves the De Rham cohomology class of the initial data, thus giving
a topologycal method of constructing nontrivial L^{2} harmonic forms on
certain manifolds with ``rich'' topology. Using Gaffney`s ``heat
flow'' the author of the present paper gives a nice geometrical
interpretation of the vanishing of the L^{2} cohomology space and also
proves that a conformal change of metric in the case of the hyperbolic
space has no effect on the L^{2} cohomology.
 A. FRASER, Brown University
Fundamental groups of manifolds with positive isotropic curvature

Positive isotropic curvature (PIC) is a natural and much studied
curvature condition which includes manifolds with pointwise
quarterpinched sectional curvatures and manifolds with positive
curvature operator. By results of Micallef and Moore there is only one
topological type of compact simply connected manifold with PIC; namely
any such manifold must be homeomorphic to a sphere. On the other hand,
there is a large class of nonsimply connected manifolds with PIC. An
important open problem has been to understand the fundamental group of
manifolds with PIC. In this talk we describe a new result in this
direction. The techniques used involve minimal surfaces.
 JACQUES HURTUBISE, CRM
Gbundles over an elliptic curve and dynamical rmatrices

The rmatrix formalism of integrable systems ties in very nicely with
the geometry of rigid bundles over a curve. Recently, through work of
Felder, Etingopf and Varchenko, this formalism was extended to a
particular nonrigid case, that of Gbundles over an elliptic curve.
In joint work with Markman, the geometry of these systems is examined,
and a description is given of the Poisson geometry, as well as a proof
of integrability.
 X. LIU, Notre Dame
Solving universal equations in GromovWitten invariants

Universal equations for GromovWitten invariants are obtained from
relations in homology classes of moduli spaces of stable curves. When
the underlying manifolds have semisimple quantum cohomology, the
generating functions of genus2 GromovWitten invariants can be
explicitly expressed in terms of genus0 and genus1 invariants by
solving already existing universal equations. These equations can also
be used to study the Virasoro conjecture.
 P. LU, Deparment of Mathematics, McMaster University, Hamilton,
Ontario L8S 4K1
CheegerGromov type compactness theorem on oribifolds

We will discuss the generalization of CheegerGromov type compactness
theorem to orbifolds. We will also discuss a compactness theorem on
orbifolds in Ricci flow.
 D. MATESSI, Centre de Recherche Mathematiques, Universite de Montreal,
Montreal, Quebec
Families of special Lagrangian tori

We will show some ways to construct isometric embeddings of
one or two parameter families of special Lagrangian submanifolds.
As an application we show that in dimension 3, the moduli space
of special Lagrangian tori is not in general ``special Lagrangian''
in the sense of Hitchin, as it is instead in dimension 2.
 M. WANG, McMaster University, Hamilton, Ontario L8S 4K1
Painleve analysis, Diophantine conditions, and special holonomy

I will report on joint work with A. Dancer of Jesus College, Oxford.
We apply the method of S. Kowalevskaya as further developed by
Painlevé, and modern authors such as Ablowitz, Ramani, and Segur to a
quadratic system associated to the cohomogeneity 1 Ricciflat
equations. The existence of ``large'' families of convergent
Painlevé expansions in the cases under study leads to restrictions on
the principal orbit type, including diophantine conditions on its
dimension (e.g. existence of integral points on elliptic
curves). Some of the diophantine conditions are related to metrics
with special holonomy.
 R. WENTWORTH, Johns Hopkins University
The YangMills flow revisited

This talk will outline work in progress with G. Daskalopoulos on the
convergence properties of the YangMills flow on holomorphic vector
bundles over higher dimensional Kaehler manifolds.
 BAOZHONG YANG, Stanford University, Stanford, California 94305, USA
Analytic aspects of gauge theories in higher dimensions

I'll talk about some recent results on the analytical aspects for
YangMills theories in dimensions greater than 4. These include
singularcompactness theorems, removable singularity theorems, as well
structure of singularities.

