In this talk, the speaker will present a class of weakly non-local gravitational theories finite and unitarity at quantum level. Moreover, such class of theories is actually a range of anomaly-free conformally invariant quantum theories in the spontaneously broken phase of the Weyl symmetry. At classical level, he will show how the Weyl conformal invariance is likely able to tame all the space-time singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. This latter statement is rigorously proved by a singularity theorem that applies to a large class of weakly non-local theories. Following the seminal paper by Narlikar and Kembhavi, he will provide an explicit construction of singularity-free black hole exact solutions.
