- Lost behind the horizon
Steve showed that for the eternal BTZ black holes one has two (entangled) boundaries, as described by Kraus, Ooguri, Shenker, and the correlators include contributions from the geodesics through the bulk. For a particular choice of the points on the boundary, one expects a singularity from geodesics that become null and reflect from the future BTZ singularity.
Unfortunately, one can't see this singularity in the perturbative expansion. Nevertheless, there is a lot of interesting questions that one may start to answer once some uncertainties get resolved. Steve worked on these questions with Lukasz Fidkowski, Veronika Hubeny, and Matt Kleban, and perhaps someone else whom I will add if necessary.
Another development was the description of inflation inside AdS/CFT. Steve needed to assume the Landscape conjecture. He wanted to create a bubble of a false dS vacuum inside the AdS space. This dS bubble inflates for a long time, and the question is how it should look like in the CFT. Note that this is an example of the "universe in the bottle". Guth and Farhi have shown that such a universe in the bottle is unlikely to exist because when you trace it back, you are likely to encounter a singularity in the past. Also, some people would say that such a large universe in the bottle contradicts the Bekenstein bounds or holography.
Steve has drawn a lot of non-trivial Penrose diagrams, and he was trying to figure out which boundaries should be associated with conformal field theories living in them, and how could the observers at the boundary "measure" physics inside the inflating portion of the Universe. Many questions remain open. Some of them are related to the "decoding of the hologram". We have had discussions how difficult it is to decode the hologram or the Hawking radiation; whether the complexity is very different to decode the local physics in the bulk outside the black hole, and the local physics inside the black hole. And also the role of analytical continuation in this whole story.
The questions are exciting - and probably critical for understanding of quantum cosmology - but the answers (or the lack of answers) to many of these questions are rather frustrating, and that's a reason to stop at this moment.