


Special Structures in Differential Geometry / Structures spéciales en géométrie différentielle Org: Gordon Craig (Bishop's) and/et Spiro Karigiannis (McMaster)
 VESTISLAV APOSTOLOV, UQAM, 201 av. Président Kennedy, Montréal (QC), Canada
Extremal Kähler metrics and Hamiltonian 2forms

I will introduce the notian of a Hamiltonian 2form on a Kähler
manifold, and present classification results for compact Kähler
manifolds admitting such forms. These can be used as a tool of
obtaining new explicit examples of extremal Kähler metrics on
certain projective bundles. This is a joint work with D. Calderbank,
P. Gauduchon and C. TønnesenFriedman.
 HENRIQUE BURSZTYN, University of Toronto and Fields Institute, 100 St. George
Street, Toronto, ON M5S 3G3
Dirac structures and symmetries in symplectic geometry

Dirac structures (introduced by T. Courant and A. Weinstein about 15
years ago) generalize, simultaneously, closed 2forms, Poisson
structures, and regular foliations. The talk will discuss the
geometry of Dirac manifolds and show how Dirac geometry provides a
natural setting for the study of generalized notions of symmetries in
symplectic geometry (including the theory of quasihamiltonian spaces
and Lie groupvalued moment maps due to Alekseev, Malkin and
Meinrenken).
 ADRIAN BUTSCHER, University of Toronto
Construction of Special Legendrian Surfaces of the Sphere of
Higher Genus

A method for constructing special Lagrangians cones in C^{3}
whose links are highergenus special Legendrian surfaces in S^{5} is
to form minimal and Legendrian connected sums of multiple copies of
\operatornameSU(3)rotated Clifford tori in S^{5}, and then to consider the cones
over these objects. There are two algebraic conditions on a
collection of proposed \operatornameSU(3)rotations, such that when these
conditions hold, the construction can be carried out using a geometric
PDE argument known as gluing. Furthermore, a number of examples of
collections of \operatornameSU(3)rotations will be studied for which the
conditions do not hold, and the possibility of finding a collection of
\operatornameSU(3)rotations for which the conditions do hold will be discussed.
 BENOIT CHARBONNEAU, McGill University, Montreal
Analytic aspects of periodic instantons

Instantons are particular connections on fourmanifolds, satisfying a
partial differential equation called the antiselfdual equation. In
principle, there exist a correspondence between instantons on a
quotient of R^{4} by a translation symmetry subgroup and the solutions
to a related equation on a quotient by some dual subgroup. This
correspondence, a nonlinear analog of the Fourier transform, is
called the Nahm transform and provides a better understanding of the
spaces of instantons.
 GORDON CRAIG, Bishop's University, Lennoxville, Quebec
Dehn Fillings and Asymptotically Hyperbolic Einstein
Manifolds

I will describe a gluing construction which allows one to fill in the
cusps of certain infinitevolume, noncompact hyperbolic manifolds in
such a way as to obtain infinitely many asymptotically hyperbolic
Einstein manifolds with a shared conformal infinity.
 DAVID DUCHEMIN, UQAM, C.P. 8888, Centreville, Montréal (Québec), H3C 1P8
Quaternionic contact structures in dimension 7

The conformal infinity of a quaternionicKähler metric on a
4nmanifold with boundary is a codimension 3distribution on the
boundary called quaternionic contact. I will describe this contact
geometry and its links with special riemannian geometry. Especially,
I prove a criterion for quaternionic contact structures on
7dimensional manifolds to be the conformal infinity of a
quaternionicKähler metric, although there is no obstruction in
greater dimensions.
 MARCO GUALTIERI, Fields Institute, Toronto
Generalized geometry

I will provide an introduction to the new field of generalized
geometry, initiated by Hitchin (math.DG/0209099) and developed in my
thesis (math.DG/0401221). I will concentrate mainly on generalized
complex geometry, which is a unification of complex and symplectic
geometry. I will make some comments about the implications for mirror
symmetry. If time permits I will speak about generalized Riemannian
and Kahler geometry.
 PENGFEI GUAN, McGill University
Conformal deformation of Ricci tensor

We report a recent work in conformal geometry jointly with G. Wang.
The lower bound of Ricci curvature tensor plays an important role in
Riemannian geometry. The problem we are interested is the conformal
deformation of the smallest eigenvalue of the Ricci tensor. The
problem is equivalent to solving an interesting fully nonlinear equation
which is uniformly elliptic, but the operator is only Lipschitz. The
equation is similar to the Yamabe equation and we encounter a similar
noncompactness difficulty. We use some geometry, e.g., Aubin and
Schoen's resolution of the Yamabe problem and the BishopGromov volume
comparison theorem. And in analysis part, we establish the local
gradient estimates and make use of Caffarelli's fundamental
C^{2,a} estimates for these type of fully nonlinear equations.
We will also discuss geometrical applications.
 MARIANTY IONEL, McMaster University
Families of Calibrated 4folds

I will discuss a result of mine in classifying the special Lagrangian
4folds in C^{4} whose second fundamental form has a nontrivial
SO(4)stabilizer at each point. Points on special Lagrangian
4folds where this stabilizer is nontrivial are the analogs of the
umbilical points in the classical theory of surfaces. I will also
talk about the case of Cayley 4folds in R^{8} with a certain
pointwise symmetry on their second fundamental form, which is work in
progress.
 NIKY KAMRAN, McGill University, Montreal, Canada
Decay of scalar waves in Kerr geometry

I shall report on some significant recent progress in the study of the
long term behavior of scalar waves in the Kerr geometry of a rotating
black hole in equilibrium, including decay theorems.
This is joint work with Felix Finster, Joel Smoller and ShingTung
Yau.
 SPIRO KARIGIANNIS, McMaster University
Properties of Moduli Spaces of G_{2} Metrics

I will discuss some properties of the moduli space of G_{2}metrics on
a G_{2}manifold, emphasising the relations and differences with the
properties of the moduli space of CalabiYau metrics.
This is a preliminary report on joint work with NaiChung Conan Leung.
 MAUNG MINOO, McMaster University, Hamilton, ON L8S 4K1
Calibrated cycles in vector bundles with special holonomy

In this talk we will report on a simple new way of constructing
calibrated cycles in certain vector bundles over the sphere and
complex projective space equipped with metrics of special holonomy
discovered by Calabi, Stenzel, Bryant and Salamon. This is joint work
with S. Karigiannis. We will also explain, in the G_{2} and
Spin(7) case, how the metrics and the cycles are related to each
other as circle lifts.
 RUXANDRA MORARU, Fields Institute
Hypercomplex structures on instanton moduli spaces

In this talk, we describe how hypercomplex structures arise on moduli
spaces of instantons over locally conformally hyperkähler
manifolds. We also discuss how these hypercomplex structures relate
to the natural Poisson structures that exist on the moduli. This is
work in progress.

