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During the last 20 years, we have seen a tremendous development in the computational power of our devices. We have by now laptops and phones that are more powerful than the high-profile workstations of a few generations ago. This computational power has already severely impacted our lives and many scientific fields as well, with examples ranging from AI to biophysics. On the other hand, a large class of problems in the study of quantum many-body systems has benefited only marginally from these developments.In the talk, I will review this class of problems, emphasizing the conceptual reason behind the limited impact that traditional computational methods have brought. I will then move on to describe the most promising candidates (in my opinion) to overcome the current situation.

Advanced subjects and complicated applications. Applications to the interacting theories. Appelquist and Carazzone theorem in QED. Decupling of massive degrees of freedom in polynomial higher derivative quantum gravity: mixed diagrams. Non-local theories of quantum gravity. On the possibility of the universal IR limit in quantum gravity

Basic calculations and basic results. One-loop Feynman diagrams and derivation of the nonlocal form factors for the two-point function. High-energy and low-energy limits. Quadratic decoupling in the IR. Curved-space calculation using the heat-kernel solution. Applications to the fourth-derivative terms in the one-loop effective action of gravity

In this talk I will describe recent proposed experimental setups developed to test the quantum nature of gravity and how they can be used to test different quantum theories. After a brief overview of the motivations behind those setups, I will show how, in the context of canonical quantum gravity, one can derive quantum gravitational corrections for an approximate Schrödinger equation for matter fields in a fixed background. The corrections can be non-linear and non-Hermitian, which poses a series of problems. I will focus on the non-Hermitian terms, their interpretation and their possible observational consequences in different scenarios. I will then describe the differences in the pilot-wave approach to quantum gravity, how it offers a natural interpretation for the corrections in terms of the Quantum Equilibrium Hypothesis and a path for deriving the effects of such corrections in tabletop experiments. If there is time, I will comment on the nonlinear modifications of the Schrödinger equations, on a recent attempt to introduce them in the path integral formalism of EFT quantum gravity in a consistent manner (Correlated Worldline Theory) and on their phenomenological consequences.

Beyond Einstein’s theory. Higher derivative theories of Gravity. Singularities and black holes. Models of Inflation. Consistency checks. Kallen-Lehmann representation. Horava-Lifshitz theories. Infrared problems. Other approaches.