Convergence and new perspectives in perturbative algebraic quantum field theory

In this talk I will present recent results obtained within the
framework of perturbative algebraic quantum field theory. This novel
approach to mathematical foundations of quantum field theory allows to
combine the axiomatic framework of algebraic QFT by Haag and Kastler with
perturbative methods. Recently also non-perturbative results have been
obtained within this approach. I will report on these results and present
new perspectives that they open for better understanding of foundations of
QFT.