Quantum Field Theories (QFTs) defined on anti-de Sitter (AdS) space have far reaching applications. The AdS/CFT correspondence is a duality between the QFT defined on the bulk of AdS and the CFT living on the boundary of AdS. This duality is extremely powerful in that one can often perform explicit computations on one side of the duality, where the other side of the duality is computationally intractable. The most famous (and interesting) application is for the study of quantum gravity. However, one can also study non-gravitational QFTS defined on AdS. Putting a QFT on AdS is a very convenient way to define a conformal theory living on its boundary. One can then use the powerful conformal bootstrap techniques. By changing the curvature radius of AdS, one can study Renormalization Group (RG) flows. By taking a "flat-space limit" of AdS, one can obtain results for the same QFT in ordinary Mikowski space (e.g scattering amplitudes). I will discuss explicit computations of Feynman-Witten diagrams in AdS. I will also discuss some non-perturbative computations for QFTs on AdS that have interesting strong-coupling phenomena such as bound states and resonances.

 The recording of the seminar is accessible here.