Abstracts

Christian Baer (Potsdam)
Generalized Cylinders and Applications

Résumé / Abstract:
We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory.
It has the advantage of being very simple and the result directly extends to semiRiemannian manifolds and to embeddings into spaces of constant
curvature. We also give a new way to identify spinors for different metrics and to derive the variation formula for the Dirac operator. Moreover, we
show that generalized Killing spinors for Codazzi tensor are restrictions of parallel spinors. Finally, we study the space of Lorentzian metrics and
give a criterion when two Lorentzian metrics on a manifold can be joined in a natural manner by a 1parameter family of such metrics.

Charles Boyer (Albuquerque)
Algebraic Geometry, Sasakian Geometry and Einstein Metrics on Spheres

Résumé / Abstract:
I outline a procedure of K. Galicki and myself that uses methods of algebraic geometry to prove the existence of SasakianEinstein
metrics on certain odd dimensional manifolds arising as the total space of generalized Seifert bundles over projective algebraic varieties with
orbifold structures. I then describe joint work with J. Kollár and K. Galicki which uses this procedure to produce a plethora of Einstein metrics on
odd dimensional spheres including exotic spheres. Many of these Einstein structures occur with huge moduli spaces, and they give the first known
examples of Einstein metrics on exotic spheres.

Robert Bryant (Duke)
Existence and uniqueness for gradient KaehlerRicci solitons

Résumé / Abstract:
Some observations about the local and global generality of gradient Kahler Ricci solitons will be made, including the existence of a
canonically associated holomorphic volume form and vector field, the local generality of solutions with a prescribed holomorphic volume form and
vector field, and the existence of Poincare coordinates in the case that the
Ricci curvature is positive and the vector field has a fixed point.

David Calderbank (Edinburgh)
Toric Differential Geometry

Résumé / Abstract:
Toric structures arise in various contexts in differential geometry and provide a method for constructing many examples of geometric
structures. They also play a role in some of Paul's most recent research. I will introduce the topic and discuss some examples.

JeanPierre Demailly (Grenoble)
Towards transcendental holomorphic Morse inequalities

Résumé / Abstract:
A generalization of holomorphic Morse inequalities to the case of transcendental (1,1)classes on general compact Kaehler
varieties will be discussed. We will explain strategies to try to get such results, as well as potential applications to the structure of the geometry
of compact Kaehler manifolds.

Thomas Friedrich (Berlin)
Characteristic torsions of geometric structures

Résumé / Abstract:
click here for abstract in Postscript format

Nigel Hitchin (Oxford)
Instantons and bihermitian metrics

Résumé / Abstract:
We show how the moduli space of antiselfdual connections on a compact 4manifold with bihermitian structure inherits a bihermitian
structure itself. Our approach is via generalized Kaehler manifolds and holomorphic Poisson structures play a key role.

Claude LeBrun (Stony Brook)
SelfDual Metrics, Closed Geodesics, and Holomorphic Disks

Résumé / Abstract:

Simon Salamon (Torino)
Eightdimensional quaternionic geometry

Résumé / Abstract:
A classification of Sp(2)Sp(1) structures on an 8manifold according to their torsion leads one to consider both the `integrable' and
`symplectic' cases. We shall describe the standard locally symmetric spaces in an unusual way using real Grassmannians of various dimensions. This
leads to the reduction and construction of examples with a closed invariant 4form.