Flat space holography, if there really is such a thing, is intimately related to Carrollian geometry. I will give an introduction to Carrollian geometry, and discuss how many Carrollian spaces of interest arise as homogeneous spaces of the Poincaré group. Finally, I will discuss the construction of Cartan geometries modelled on these spaces.

The canonical example of AdS/CFT relates N=4 SYM in 4d to supergravity on AdS5 x S5 by considering a stack of D3-branes. A natural question then emerges: what about considering other Dp-branes? The worldvolume theory is again SYM but is not conformal anymore, while the supergravity dual is now only conformally AdS. Despite these differences, some control remains, and some inspiration from the p=3 case can be sought. In this talk, I will review this setup and discuss the recent results of [2503.18770] and [2503.14685] regarding the computation of correlation functions.

For this JC, I will review the recently much debated puzzles that arise in holographic systems with baby universes. After describing the original set-up of Antonini-Sasieta-Swingle, I will explain the paradox raised by Antonini-Rath, which suggests the existence of a single CFT state that can have two distinct holographic descriptions in the bulk: one with a closed baby universe and one without. I will discuss various proposed resolutions of this puzzle, which may (or may not) require us to rethink the holographic dictionary in AdS/CFT.