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 \begin{equation*} \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 \ldots \mathrm{d}s_n, \quad t \geq 0, \end{equation*} as analytic semigroups. Here, $H \geq 0$ 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.