The thesis will focus on the study of the properties of holographic quantum field theories on curved background, with the applications to cosmology and to quantum field theories with defects.

 The holographic duality is a relation between a quantum field theory (QFT) on a d-dimensional spacetime (which may be curved) and a gravitational theory on a different, higher-dimensional spacetime. In appropriate limits, classical general relativity in higher dimensions can be used to compute quantities in the lower-dimensional QFT in the strongly-coupled regime. The thesis project will include application of this idea in several contexts:

 1) Holographic QFTs on cosmological spacetimes such as de Sitter and Freedman-Lemaitre-Robertson-Walker (FLRW). This will include the holographic calculation of de Sitter correlation functions in various coordinate systems (cosmological, static...), understanding their relations, investigating applications to cosmology (primordial inflation, production of primordial back holes and reheating at strong coupling) and more generally the structure of non-perturbative physics on de Sitter and FLRW spacetimes.

 2) Holographic QFTs on spacetimes of constant negative curvature.  These theories can be mapped, by a conformal transformation, to QFTs with defects, or to interfaces between two different QFTs. Holography can be used to compute correlation functions and renormalization group (RG) flows involving operators which are inserted on the defect (or interface), generalizing the standard notion of RG flow to theories with broken translation symmetry.  Defect dynamics is important in all quantum field theories as they are generated by non-local operators like Wilson lines and 't Hooft lines.