Spectral shift functions for differential operators.

We will discuss extensions of the Lifshits-Krein-Koplienko spectral shift functions to cases of more general operators that include some classical differential operators

Multiple operator integrals and their applications.

Multiple operator integrals are multilinear transformations on operators that naturally arise as remainders of Taylor approximations of operator functions and also as extensions of Schur multipliers to a multilinear case. Theory of multiple operator integrals has been developing for over 60 years and has accumulated a number of important results and interesting applications. We will discuss recently established analytic properties of these transformations and their applications to perturbation theory