On the determinant of Gauss-Manin connections and hypergeometric functions of hypersurfaces.
On the geometry of free loop spaces.
On the principal bundles over a flag manifold.
On the torsion of spaces with connection
Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface (II).
In [6], orbifold G-bundles on a certain class of elliptic fibrations over a smooth complex projective curve X were related to parabolic G-bundles over X. In this continuation of [6] we define and investigate holomorphic connections on an orbifold G-bundle over an elliptic fibration.
Poisson geometry of flat connections for SU(2)-bundles on surfaces.
Pseudo-real principal Higgs bundles on compact Kähler manifolds
Let be a compact connected Kähler manifold equipped with an anti-holomorphic involution which is compatible with the Kähler structure. Let be a connected complex reductive affine algebraic group equipped with a real form . We define pseudo-real principal -bundles on . These are generalizations of real algebraic principal -bundles over a real algebraic variety. Next we define stable, semistable and polystable pseudo-real principal -bundles. Their relationships with the usual stable, semistable...
Removable singularities for the Yang-Mills-Higgs equations in two dimensions
Scalar curvature and connected sums of self-dual 4-manifolds
Under a reasonable vanishing hypothesis, Donaldson and Friedman proved that the connected sum of two self-dual Riemannian 4-manifolds is again self-dual. Here we prove that the same result can be extended to the positive scalar curvature case. This is an analogue of the classical theorem of Gromov–Lawson and Schoen–Yau in the self-dual category. The proof is based on twistor theory.
Seiberg-Witten Theory
We give an introduction into and exposition of Seiberg-Witten theory.
Singular Yang-Mills connections
Singular Yang-Mills fields. Local theory I.
Singular Yang-Mills fields. Local theory II.
Smooth metric measure spaces, quasi-Einstein metrics, and tractors
We introduce the tractor formalism from conformal geometry to the study of smooth metric measure spaces. In particular, this gives rise to a correspondence between quasi-Einstein metrics and parallel sections of certain tractor bundles. We use this formulation to give a sharp upper bound on the dimension of the vector space of quasi-Einstein metrics, providing a different perspective on some recent results of He, Petersen and Wylie.
Some remarks on almost Kenmotsu manifolds.
Sous-groupes discrets des groupes de Lie : rigidité, arithméticité
Stability of the tangent bundle and existence of a Kähler-Einstein metric.
Structures de Weyl admettant des spineurs parallèles
Structures de Weyl et théorèmes d'annulation sur une variété conforme autoduale
Symmetric Polynomials Constructed From Moduli of Stable Sheaves with odd c1 on ruled surfaces.