Chaire d'Excellence (20082012)
Cette page est un journal où sont publiées les actions financées par la
Chaire d'Excellence "Géométrie et Topologie via la Théorie de Jauge"
(GETOGA) décernée par l'
Agence Nationale de la Recherche (ANR).
A conference will be held at Nantes University from may 21st to 25th 2012 to celebrate Bogolomov's 65th birthday.
See the web site for more informations.
Postdoctoral fellowships
Two more fellowships in mathematics have been created thanks to the Chaire
d'Excellence GETOGA (1 year teaching free position). Congratulations to
 Reza Rezazadega (arriving in sept 2011)
 Roberto Mossa (arriving in jan 2012)
who is joining
Jean Leray Laboratoire.
A special
trimester on Contact and Symplectic Topology will be held at
Nantes University during the summer 2011. The focus of the trimester will be on
 Interactions between contact topology, symplectic geometry and lowdimensional topology,
 Applications of gauge theory and Heegaard Floer homology to contact topology
 Contact homology and Symplectic Field Theory
 Contact topology in higher dimension
 Floer homologies
A
conference on extremal metrics will be held at the CIRM in Luminy,
from the 7th to 12th of February 2011.
The conference will present the new developments in the study of
canonical/special metrics that can be considered as uniformisers of
complex geometry (like constant scalar curvature Kaehler metrics,
extremal Kaehler metrics, KaehlerEinstein metrics, KaehlerRicci
solitons, SasakiEinstein metrics, Bergman metrics, balanced metrics
...). It will also reflect the diversity of analytic methods
to construct such metrics (flows, continuity methods, gluing
techniques, ...)
and the diversity of varieties where they live (compact and non compact Kaehler
manifolds, Sasaki manifods, toric manifolds, spherical manifolds, orbifolds,...).
Finally, a part of the conference will be concerned with the relationship
between the existence of canonical metrics and algebraic conditions coming from
Geometric Invariant Theory.
Invited Professors at Laboratoire Jean Leray
 Claire Voisin (IHES CNRS, 27/11/09)
 Geometry seminar: Algèbres de cohomologie des variétés kählériennes
 Julien Keller (Université de Provence, 10/11/0911/12/09)
 Misha Verbitsky (02/11/0913/11/09)
 Three lectures: on Sasakian manifolds and locally conformally Kaehler geometry
1. Sasakian and CRgeometry
2. Structure theorem Vaisman manifolds
3. Embedding theorem for Sasakian manifolds
Abstract:
Sasakian manifolds are Riemannian manifolds
equipped with an $\R$equivariant Kaehler structure
on their Riemannian cone. This allows one to characterize
the Sasakian manifolds in terms of Kaehler structure on
the corresponding cones. Three lectures are planned:
1. A characterization of Sasakian manifolds in terms
of CRgeometry. 2. Locally conformally Kaehler
geometry, Vaisman manifolds and the structure theorem,
providing an equivalence of Vaisman geometry and
Sasakian geometry. 3. A version of Kodaira
theorem for Sasakian and Vaisman manifolds,
giving a complex embedding of a Vaisman manifold
into a Hopf manifold and a CRembedding of a
Sasakian manifold into a sphere. These results
are obtained jointly with Liviu Ornea.
 Stefan Bauer (Bielefeld University, 05/09/0909/09/09)
 Topology seminar:
Proper maps between Frechet spaces
Abstract:
The space of smooth sections of a bundle over a compact manifold is the paradigm of a nuclear Fréchet space, graded by Sobolev norms . Nuclear Fréchet spaces, as is well known, are similar to finite dimensional vector spaces. For example, compact subsets are characterised by the HeineBorel property: A subset of a nuclear Fréchet space is compact iff it is closed and bounded.
Homotopy classes of proper maps between finite dimensional vector spaces are closely related to homotopy groups of spheres via onepoint compactifications. The concept of onepoint compactifications does not extend neatly to the infinite dimensional setting. Homotopy classes of proper maps, however, remain closely related to homotopy groups of spheres, as will be put in concrete terms.
 Geometry Seminar : Refined SeibergWitten invariants
Abstract:This talk is a survey of applications of the stable homotopy approach to SeibergWitten theory.
A
special trimester on Kähler and related geometries will be held at
Nantes University from september
to december 2009. The topics of interest are
 Calabi programme, Extremal, KählerEinstein metrics
 Relation with stability
 Special Holonomy
 Sasakian geometry
 etc..

Postdoctoral fellowships
Two fellowships in mathematics have been created thanks to the Chaire
d'Excellence GETOGA (2 years teaching free positions). Congratulations to
 Andrew Clarke (arriving in sept 2009), and
 Sheila Sandon (arriving in jan 2010)
who are joining
Jean Leray Laboratoire.
Another one year postdoctoral position is awarded by the CNRS together with the Chaire d'Excellence. Congratulation to
who is joining the
Laboratoire Jean Leray from oct 2009.