Hochschild homology and Riemann-Roch formula for matrix factorizations

Using Eisenbud's category of matrix factorizations,
isolated hypersurface singularities can be viewed
as smooth non-commutative spaces. In this picture,
the Milnor algebra of the singularity plays the role
of the de Rham cohomology of the space
(interpreted as the Hochschild homology of the
category of matrix factorizations).
We will also describe the Chern character map
and an analog of the Hirzebruch-Riemann-Roch formula
for computing the Euler characteristic of the
Hom-space between two matrix factorizations.
The talk is based on a joint work with Alexander Polishchuk.