Motivated in part by the difficulties facing a quantum theory of gravity, Nobel Prize laureate G.'t Hooft has argued that quantum mechanics cannot provide a definitive description of the microscopic world. 't Hooft argues that, underlying quantum mechanics, a deeper level theory must exist, which must be deterministic, as opposed to the fundamental indetermism of quantum theory. Moreover, standard quantum mechanics must emerge as an effective theory out of this more fundamental theory. We will first review 't Hooft's arguments. Then we will briefly present our own contribution to this research line.

I will give an outlook of open string field theory (OSFT), as a model for D-branes dynamics. This model provides a new approach to boundary conformal field theory (BCFT) where, for example, Boundary States are build from open string gauge invariants. I discuss some elementary classical solutions and their interpretations as D-branes, in the bosonic string. Finally I present a recently discovered analytic solution which connects any two given D-branes configurations. This includes solutions with higher energy than the starting background ("climbing up" the worldsheet boundary RG-flow), and multi-branes solutions which dynamically generate Chan-Paton's factors out of a single D-brane. OSFT background independence from the initially chosen WS boundary conditions is achieved by shifting the string field on the classical solution, plus an elementary field-redefinition.

I will discuss new techniques that allow one to make progress in establishing holographic dualities for Lifshitz space-times (at the gravitational level) for which there is no relation (like dimensional reduction) to an AdS space-time. This provides us with a real non-AdS setting in which we can do holographic calculations. One of the main reasons that this is possible has to do with the realization that the boundary geometry is not a Riemannian geometry but rather something called Newton-Cartan geometry. I will introduce this geometric structure in a step by step fashion. I will conclude with some comments related to work in progress towards extending such ideas to other non-AdS space-times such as Schroedinger space-times.

I review a method for constructing non-extremal stationary solutions of $N=2$ supergravity, which is based on dimensional reduction over time and the real formulation of special geometry. As an application, I discuss four-dimensional non-extremal Nernst branes and their lift to five dimensions.

In this talk I describe scattering processes of gravitons in quantum gravity, both form the field theory and also from the string theory point of view. We will define a particular kinematical regime, where the energies of the two incoming gravitons are Trans-Planckian, and where at the same time the number $N$ of gravitons in the final state is very large. As we will argue, these $2$ to $N$ scattering amplitudes support the the idea that a black hole is produced, which is a bound state of $N$ gravitons in a quantum critical state. We will also argue that this picture has to be refined at extremely large energies, where an interesting transition from field theory to string theory takes place.

We carry out a systematic study of entanglement entropy in nonrelativistic conformal field theories via holographic techniques. After a discussion of recent results concerning Galilean conformal field theories, we deduce a novel expression for the entanglement entropy of $(1+1)$-dimensional Lifshitz field theories — this is done both at zero and finite temperature. Based on these results, we pose a conjecture for the anomaly coefficient of a Lifshitz field theory dual to new massive gravity. It is found that the Lifshitz entanglement entropy at finite temperature displays a striking similarity with that corresponding to a flat space cosmology in three dimensions. We claim that this structure is an inherent feature of the entanglement entropy for nonrelativistic conformal field theories. We finish by exploring the behavior of the mutual information for such theories.

The partition function of topological string theory on a Calabi-Yau threefold is defined perturbatively as a sum over free energies of genus g Riemann surfaces. I will review the construction of a differential ring of special functions on the moduli space of CY threefolds. I will show that the higher genus amplitudes can be expressed as polynomials in the generators of this ring, which significantly simplifies a Feynman diagram computation. The polynomial structure of the amplitudes can furthermore be exploited to determine specific monomials to all orders in perturbation theory. A universal Airy differential equation in the topological string coupling can be derived governing these monomials. Solutions of this equation also offer hints of non-perturbative topological strings.