Pablo A. Cano (University of Murcia)

The prediction of singularities is one of the most fundamental open problems of general relativity. While phenomenological models of singularity-free black holes have long been postulated in the literature, a dynamical theory supporting such geometries is often absent. Recently, this situation has changed thanks to the explicit construction of extensions of GR with infinite towers of higher-derivative corrections that can resolve black hole singularities in a fully dynamical way. I will review the main achievements and the status of this program and I will discuss some of the current challenges.