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 semi-Riemannian 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 1-parameter family of such metrics.
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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 Sasakian-Einstein 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.
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Robert Bryant (Duke)
Existence and uniqueness for gradient Kaehler-Ricci 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.
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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.
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Jean-Pierre 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.
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Thomas Friedrich (Berlin)
Characteristic torsions of geometric structures
Résumé / Abstract: click here for abstract in Postscript format
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Nigel Hitchin (Oxford)
Instantons and bihermitian metrics
Résumé / Abstract: We show how the moduli space of anti-self-dual connections on a compact 4-manifold with bihermitian structure inherits a bihermitian structure itself. Our approach is via generalized Kaehler manifolds and holomorphic Poisson structures play a key role.
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Claude LeBrun (Stony Brook)
Self-Dual Metrics, Closed Geodesics, and Holomorphic Disks
Résumé / Abstract:
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Simon Salamon (Torino)
Eight-dimensional quaternionic geometry
Résumé / Abstract: A classification of Sp(2)Sp(1) structures on an 8-manifold 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 4-form.
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