Using the BF formulation of JT gravity, we will extend the factorisation techniques in BF theory with compact groups to non-compact ones. The Euclidean path integral formulation of these theories provides some locality interpretation of these results in terms of gravitational edge modes. We shall comment on how to extend these ideas to 3d gravity. We will aim to stress differences occurring between gauge and gravity theories already in these low dimensional examples.

The extremal limit of single R-charged AdS5 black holes in type IIB is known to be described by a system of N free fermions in a one dimensional harmonic oscillator potential. Since the quantum mechanical problem is solvable and its phase space formulation appears in the gravity dual (LLM geometries), it allows us to explore the relation between entanglement, quantum correlation design and connectivity in space in this set-up, both in a single and a two boundary situation.

The relation between black holes and thermodynamics leading to the holographic principle is well known. Formulating thermodynamics as the theory of transformations performing some work or task allows us to reinterpret recent developments in AdS/CFT, such as the holographic description of entanglement entropy, as a measure of the connectivity of space (resource). Whether spacetime in the interior of a black hole also allows an understanding as a resource is an interesting open question.

Motivated by either condensed matter or quantum gravity holographic considerations, I will discuss some preliminary work on how to compute the time evolution in Renyi entropies in 2d CFTs in the large c limit for thermal states perturbed by localized primary operators. Time permitting, I will comment on the potential relation between this work and previous holographic calculations in the context of the EPR=ER conjecture.

I will review some recent attempts at providing a microscopic description for extremal black holes. First, I will explain a constituent model for extremal non-rotating non-BPS asymptoticaly flat black holes. Second, I will summarise the main claims in the so called extremal BH/CFT correspondence, pointing out how a chiral CFT can emerge as a limit of a non-chiral CFT. Finally, I will use R-charge AdS black holes to derive the existence of emergent IR CFTs, similar to the ones that have been argued to capture some interesting quantum criticality phenomena in some strongly coupled condensed matter systems.

I will review some recent attempts at providing a microscopic description for extremal black holes. First, I will explain a constituent model for extremal non-rotating non-BPS asymptoticaly flat black holes. Second, I will summarise the main claims in the so called extremal BH/CFT correspondence, pointing out how a chiral CFT can emerge as a limit of a non-chiral CFT. Finally, I will use R-charge AdS black holes to derive the existence of emergent IR CFTs, similar to the ones that have been argued to capture some interesting quantum criticality phenomena in some strongly coupled condensed matter systems.