# A review of constructive algebraic quantum field theory (Gandalf Lechner, FAU)

The mathematically rigorous construction of quantum field theories

beyond perturbation theory is one of the main challenges of QFT. In this talk

I will review approaches to this problem that are based on concepts from

"algebraic quantum field theory" (AQFT), a framework based on algebras of

observables localized in open regions in spacetime instead of point-like

localized quantum fields. The talk will hence also present the main features of

AQFT and review ideas, results and open problems in the subject.