Fermionic integration and perturbations of semigroups

In this talk I will explain an algebraic machinery, based on Fermionic integration, which basically allows to rewrite expressions of the form $${\int }_{t{\sigma }_n}{e}^{-s_{1}H}{P}_1{e}^{-(s_2-s_1)H}{P}_2\dots e^{-(s_n-s_{n-1})H}{P}_n{e}^{-(t-s_n)H}\mathrm{d}{s}_1\dots \mathrm{d}{s}_n,t\ge 0,$$ as analytic semigroups. Here, $H\ge 0$ is an unbounded self-adjoint operator and each $P_j$ is an unbounded possibly non-self-adjoint operator. Applications to noncommutative geometry will be presented. This is joint work with Batu Güneysu.