Natural operations on the Hochschild cohomology

The talk will be devoted to the problem of classification of all natural operations acting on the Hochschild cohomology of an associative algebra, by which one usually means the understanding of the homotopy type of the operad B formed by these operations. We will explain what a "natural operation" is and present two equivalent definitions of completely different natures. We then describe the homotopy type of B and show how is this descrition related to the Deligne Hochschild cohomology conjecture.