A local analytic splitting of the holonomy map on flat connections.
A nonlinear Poisson transform for Einstein metrics on product spaces
We consider the Einstein deformations of the reducible rank two symmetric spaces of noncompact type. If is the product of any two real, complex, quaternionic or octonionic hyperbolic spaces, we prove that the family of nearby Einstein metrics is parametrized by certain new geometric structures on the Furstenberg boundary of .
An index inequality for embedded pseudoholomorphic curves in symplectizations
Let be a surface with a symplectic form, let be a symplectomorphism of , and let be the mapping torus of . We show that the dimensions of moduli spaces of embedded pseudoholomorphic curves in , with cylindrical ends asymptotic to periodic orbits of or multiple covers thereof, are bounded from above by an additive relative index. We deduce some compactness results for these moduli spaces. This paper establishes some of the foundations for a program with Michael Thaddeus, to understand...
Asymptotic behavior of the L2-metric on moduli spaces of Yang-Mills connections.
Asymptotic behavior of the L2-metric on moduli spaces of Yang-Mills connections, II.
Asymptotic behaviour and the moduli space of doubly-periodic instantons
We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus with a complex line , with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing new asymptotic invariants. We show that the underlying holomorphic bundle extends to . The converse statement is also true, namely a holomorphic bundle on which is flat on the torus at infinity, and satisfies a stability condition, comes from a doubly-periodic instanton....
Classification analytique de structures de Poisson
Notre étude porte sur une catégorie de structures de Poisson singulières holomorphes au voisinage de et admettant une forme normale formelle polynomiale i.e. un nombre fini d’invariants formels. Les séries normalisantes sont divergentes en général. On montre l’existence de transformations normalisantes holomorphes sur des domaines sectoriels de la forme , où est un monôme associé au problème. Il suit une classification analytique.
Cohomologie quantique
Compactness of moduli spaces of negatively curved metrics
Conformal Imbeddings of the Complex Projective Plane and Self-Dual Connections.
Courbes pseudo-holomorphes équisingulières en dimension 4
Degeneration of Riemann surfaces and intermediate polarization of the moduli space of flat connections.
Extended moduli spaces of flat connections on Riemann surfaces.
Fibrés paraboliques stables et connexions singulières plates
Generating varieties for the triple loop space of classical Lie groups
For G = SU(n), Sp(n) or Spin(n), let be the centralizer of a certain SU(2) in G. We have a natural map . For a generator α of , we describe J⁎(α). In particular, it is proved that is injective.
Homogeneous Connections and Moduli Spaces.
Infinite geodesic rays in the space of Kähler potentials
In this paper we prove the existence of solutions of a degenerate complex Monge-Ampére equation on a complex manifold. Applying our existence result to a special degeneration of complex structure, we show how to associate to a change of complex structure an infinite length geodetic ray in the space of potentials. We also prove an existence result for the initial value problem for geodesics. We end this paper with a discussion of a list of open problems indicating how to relate our reults to the...
Infinitesimal conjugacies and Weil-Petersson metric
We study deformations of compact Riemannian manifolds of negative curvature. We give an equation for the infinitesimal conjugacy between geodesic flows. This in turn allows us to compute derivatives of intersection of metrics. As a consequence we obtain a proof of a theorem of Wolpert.
Instanton moduli as a novel map from tori to K3-surfaces.
Metaplectic quantization of the moduli spaces of flat and parabolic bundles.