A primer of group theory for Loop Quantum Gravity and Spin-foamsThe aim of a theory really is, to a great extent, that of systematically organizing past experience in such a way that the next generation, our students and their students and so on, will be able to absorb the essential aspects in as painless a way as possible, and this is the only way in which you can go on cumulatively building up any kind of scientific activity without eventually coming to a dead end.M. F. Atiyah, [Ati74].

We construct and discuss the form of the (effective) spacetime geometry inside a black hole undergoing a quantum transition to a white hole, taking into account the back-reaction of the component of the Hawking radiation falling into the hole.

The term 'locality' is used in different contexts with different meanings. There have been claims that relational quantum mechanics is local, but it is not clear then how it accounts for the effects that go under the usual name of quantum non-locality. The present article shows that the failure of 'locality' in the sense of Bell, once interpreted in the relational framework, reduces to the existence of a common cause in an indeterministic context. In particular, there is no need to appeal to a mysterious space-like influence to understand it.

At the end of Hawking evaporation, the horizon of a black hole enters a physical region where quantum gravity cannot be neglected. The physics of this region has not been much explored. We characterise its physics and introduce a technique to study it.

The possibility that a black hole could tunnel into a white hole has recently received attention.Here we present a metric that improves the 'firework' geometry: it describes this entire process and solves the Einstein equations everywhere except on a small transition surface that corresponds to the quantum tunnelling. We also explicitly compute the corresponding ray-tracing map from past infinity to future infinity. I. FIREWORKS

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We discuss the notion of coherent states from three different perspectives: the seminal approach of Schrödinger, the experimental take of quantum optics, and the theoretical developments in quantum gravity. This comparative study tries to emphasise the connections between the approaches, and to offer a coherent short story of the field, so to speak. It may be useful for pedagogical purposes, as well as for specialists of quantum optics and quantum gravity willing to embed their perspective within a wider landscape.

Time at the Planck scale (∼ 10 −44 s) is an unexplored physical regime. It is widely believed that probing Planck time will remain for long an impossible task. Yet, we propose an experiment to test the discreteness of time at the Planck scale and show that it is not far removed from current technological capabilities.