# Hirzebruch-Riemann-Roch and Lefschetz formulas for dg-categories

SPEAKER: Alexander Polishchuk

TITLE: Hirzebruch-Riemann-Roch and Lefschetz formulas for dg-categories

ABSTRACT I will describe versions of the formulas in the title in the context of noncommutative geometry (that involves replacing algebraic varieties by dg-categories). The analog of the Hirzebruch-Riemann-Roch formula computes the dimension of the space of morphisms between two objects in a dg-category in terms of their Chern characters taking values in the Hochschild homology of the category. The analog of Lefschetz formula computes the trace of the action of an endofunctor on the Hochschild homology.