In this paper we prove that on a smooth algebraic variety the HKR-morphism twisted by the
square root of the Todd genus gives an isomorphism between the sheaf of poly-vector fields …

The Atiyah class, Hochschild cohomology and the Riemannâ•fiRoch theorem Page 1 J.
London Math. Soc. (2) 79 (2009) 129–143 Cо2008 London Mathematical Society doi:10.1112/jlms/jdn064 …

We study modules over stacks of deformation quantization algebroids on complex Poisson
manifolds. We prove finiteness and duality theorems in the relative case and construct the …

We work in the setting of Calabi-Yau mirror symmetry. We establish conditions under which
Kontsevich's homological mirror symmetry (which relates the derived Fukaya category to the …

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 …

Abstract Every Fourier-Mukai equivalence between the derived categories of two K3
surfaces induces a Hodge isometry of their cohomologies viewed as Hodge structures of …

We survey the basic theory of non-commutative K3 surfaces, with a particular emphasis to
the ones arising from cubic fourfolds. We focus on the problem of constructing Bridgeland …

We combine the theory of traces in homotopical algebra with sheaf theory in derived
algebraic geometry to deduce general fixed point and character formulas. The formalism of …

The purpose of this paper is to propose an analogue of Dubrovin's conjecture [15] in a more
general setting. We shall firstly recall the original conjecture of Dubrovin in Section 1. 1. We …

Suppose one has found a non-empty sub-category $\mathcal {A} $ of the Fukaya category of
a compact Calabi-Yau manifold $ X $ which is homologically smooth in the sense of non …