Black holes: The inside story of gravitational collapse
What does the interior of a black hole look like? Beyond the astrophysical motivation, it turns out that answering this question is at the heart of profound conjectures in General Relativity. One of them is the celebrated Penrose’s Strong Cosmic Censorship Conjecture supporting the deterministic character of the theory of gravitation. I will present recent advances on this topic, based on modern techniques in hyperbolic PDEs and Differential Geometry, and describe outstanding problems.