I will discuss recent work on the numerical conformal bootstrap that modifies the scope of the so-called truncation methods and improves their efficiency. I will show how the proposed approach performs in the recently discussed context of bootstrability for 1d defect CFTs on 1/2 BPS Wilson lines in 4d N=4 SYM theory, how it compares with the more standard linear functional method and how different algorithms allow us to tackle the large-scale non-convex optimization problems that are involved in this method. Along the way, I will address the prospects of AI and Machine Learning in this particular direction.

I will discuss recent work on the supergravity description of the fully localized orthogonal black M2-M5 intersection using blackfold theory. Special emphasis will be given to the near-extremal thermodynamics of this system from which we can read off, for the first time, the large-N scaling of the central charge of the two-dimensional superconformal field theory that lives at the intersection. The resulting formula for this central charge is suggestive for the underlying M2 and M5 brane physics.