For an arbitrary differential graded algebra A with finite-dimensional total cohomology we
introduce a pairing on the Hochschild homology of A, derive an explicit formula for the Chern …

R.–Soit D un opérateur différentiel holomorphe opérant sur les sections d'un fibré vectoriel
holomorphe sur une variété complexe de dimension n. Nous démontrons une formule …

We give an explicit formula for sp 2 n-basic representatives of the cyclic cohomology of the
Weyl algebra HC•(A 2 n). As an application, we prove a generalization of a theorem of Nest …

Let D be a holomorphic differential operator acting on sections of a holomorphic vector
bundle on an n-dimensional compact complex manifold. We prove a formula, conjectured by …

We introduce a notion of Hochschild Lefschetz class for a good coherent D-module on a
compact complex manifold, and prove that this class is compatible with the direct image …

Let X be a smooth projective complex variety. The Hochschild homology HH•(X) of X is an
important invariant of X, which is isomorphic to the Hodge cohomology of X via the …

Let E be a holomorphic vector bundle on a complex manifold X such that dim CX= n. Given
any continuous, basic Hochschild 2n-cocycle ψ 2n of the algebra Diff n of formal …

Integration over complex manifolds via Hochschild homology Page 1 J. Noncommut. Geom. 3
(2009), 27–45 Journal of Noncommutative Geometry © European Mathematical Society …

My research interests involve various aspects of algebraic geometry, noncommutative
geometry and homological algebra. During my post-doctoral appointment in the past two …