Natural 2-forms on the tangent bundle of a Riemannian manifold
Non compact boundaries of complex analytic varieties in Hilbert spaces
We treat the boundary problem for complex varieties with isolated singularities, of complex dimension greater than or equal to 3, non necessarily compact, which are contained in strongly convex, open subsets of a complex Hilbert space H.We deal with the problem by cutting with a family of complex hyperplanes and applying the already known result for the compact case.
Noncommutative Borsuk-Ulam-type conjectures
Within the framework of free actions of compact quantum groups on unital C*-algebras, we propose two conjectures. The first one states that, if is a free coaction of the C*-algebra H of a non-trivial compact quantum group on a unital C*-algebra A, then there is no H-equivariant *-homomorphism from A to the equivariant join C*-algebra . For A being the C*-algebra of continuous functions on a sphere with the antipodal coaction of the C*-algebra of functions on ℤ/2ℤ, we recover the celebrated Borsuk-Ulam...
Non-commutative differential geometry
Non-commutative Hodge structures
This article gives a survey of recent results on a generalization of the notion of a Hodge structure. The main example is related to the Fourier-Laplace transform of a variation of polarizable Hodge structure on the punctured affine line, like the Gauss-Manin systems of a proper or tame algebraic function on a smooth quasi-projective variety. Variations of non-commutative Hodge structures often occur on the tangent bundle of Frobenius manifolds, giving rise to a tt* geometry.
Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations.
Nonlinear structures determined by measures on Banach spaces
Notes on differential calculus in topological liear spaces.