Non-perturbative Quantum Field Theory in curved spaces: Infrared effects in de Sitter space-time

Quantum field theory on curved space-times is a very powerful framework for the study of quantum phenomena in situations where gravitation itself can be treated classically. Of special interest is the study of interacting quantum fields  in de Sitter space-time, where corrections computed using the standard perturbative expansion are plagued by contributions that secularly grow with time and/or infrared divergences. This has motivated the consideration of alternative techniques. In this talk I will summarise  recent work on this  topic in relation to the development of non-perturbative methods to compute correlation functions in a systematic way.