The algebraic approach to quantum field theory is the leit-motiv of several breakthroughs in our understanding of the conceptual, of the constructive and of the mathematical foundations of quantum field theory. In the past 15 years, the formulation of free and perturbative quantum field theories on arbitrary curved backgrounds, the role of the renormalization group and the explicit construction of Hadamard states have been thoroughly analyzed and unsterdood in a rigorous mathematical way. Concrete applications to models ranging from cosmology, particle and solid state physics have been discussed with promising results. Furthermore, in the past 5 years, there have been new, rather successful attempts towards the construction both of interacting classical and quantum field theories as well as of local gauge theories.
Goal of the workshop is two-fold:
On the one hand it is meant as an occasion to give an overview of the status of the algebraic approach to quantum field theory and to discuss all new recent developments.
On the other hand we want to outline the main open problems and the most promising attempts to tackle them.