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Lee Smolin has argued that one of the barriers to understanding time in a quantum world is our tendency to spatialize time. The question is whether there is anything in physics that could lead us to mathematically characterize time so that it is not just another funny spatial dimension. I will explore the possibility(already considered by Smolin and others) that time may be distinguished from space by what I will call a measure of Booleanity. The Bell-Kochen-Specker Theorem shows that the statistics of quantum systems (unlike that of classical systems) do not in general permit of a Boolean substructure. I will outline reasons for thinking that time is the dimension in which the Booleanity of spacetime (considered as a quantum system) varies, while space is characterized by constant Booleanity. I will not be able to give a mathematically complete characterization of the Booleanity of a region of spacetime, since that would require nothing less than knowing how to quantize spacetime; however, I will argue that something like this is needed if one is to make any sense of an ontological distinction between past, present, and future in terms of modern physics. I will also briefly consider possible objections to this view arising from the relativity of simultaneity, which (on its usual interpretation) apparently places all events on an equal ontological footing. In order to get around this we need a generalized conception of simultaneity that treats Einstein's notion of simultaneity as a special case, and which allows for equivalence classes of spacelike separate events distinguished by covariant quantities such as action, phase, and (as I will argue) any reasonable measure of Booleanity.

Quantum operations are known to be the most general state transformations that can be applied to parts of compound systems compatibly with the probabilistic structure of quantum mechanics. What about the most general transformations of quantum operations? It turns out that any such general transformation can be realized by a quantum network with an open slot in which the input operation can be inserted, thus programming the resulting circuit. Moreover, one can recursively iterate this construction, generating an infinite hierarchy of admissible transformations and proving their realization within the circuit model of quantum mechanics. These results provide the basis of a new method to optimize quantum networks for information processing tasks, including e.g. gate estimation, discrimination, programming, and cloning. As examples of application, I will present here the optimal quantum networks for estimation of group transformations, for the alignment of reference frames with multiple communication rounds, and for universal cloning of unitary transformations.

More than 40 years ago, Bell ruled out completely local hidden variable models as an explanation for quantum correlations. However, a new type of hidden variable model has recently been brought to light by the work of Leggett. Such a model has both local and non-local parts. Roughly speaking, having a local part means that the measurement outcomes can be guessed with better than 50% success. In this talk, I will explain that there exist quantum correlations for which any hidden variable model must have a trivial local part. I will then discuss how an extension of the original theorem implies that these correlations can be used to enhance the quality of a private random string.

New spin foam models for gravity have been recently proposed to deal with the shortcomings of the Barrett-Crane model. In particular, they draw a closer connection between the Loop Quantum Gravity and the Spin Foam approaches to non perturbative quantum gravity. In this talk, I will present the construction for the case of Lorentzian signature and finite Immirzi parameter. An area operator can be defined and its spectrum agrees with the one defined in LQG. Finally, the amplitude is shown to be finite after a suitable regularization.

We give an overview of what we have called the \'LQG spinfoam models,\' that provide a spinfoam dynamics for LQG, for arbitrary values of the Barbero-Immirzi parameter in both Lorentzian and Euclidean signatures. The key motivation behind these models was to modify the Barrett-Crane model, by handling more carefully certain constraints, called simplicity constraints, which become second class in the quantum theory. As a result, the kinematics of the models exactly match those of LQG. The goal of this talk is to provide a broad picture of the significance of these models and their basic ideas.

We study various aspects of power suppressed as well as exponentially suppressed corrections in the asymptotic expansion of the degeneracy of quarter BPS dyons in N=4 supersymmetric string theories. In particular we explicitly calculate the power suppressed corrections up to second order and the first exponentially suppressed corrections. We also propose a macroscopic origin of the exponentially suppressed corrections using the quantum entropy function formalism. This suggests a universal pattern of exponentially suppressed corrections to all four dimensional extremal black hole entropies in string theory.

I will discuss the various sources of non-Gaussianity (NG) in a class of multi-field models of inflation. I will show that there is both an intrinsic and a local contribution to the NG although they both have the same shape. It is also possible in this class of models that the dominant part to the 3-pt function comes from loop diagrams. These models are of the hybrid type and while they occur naturally in string theory, the conditions for the NG to be important are not generic.

We report on recent progress in understanding string compactifications to four dimensions, preserving minimal supersymmetry. We develop a general formalism to construct the kinetic terms of the low energy degrees of freedom. At strong warping, new light Kaluza-Klein modes appear, which change the effective action for the complex and Kahler moduli. We explain how to determine these new fields starting from 10d, and find their couplings to the zero mode sector.

In two dimensional CFTs the Zamolodchikov\'s c-theorem is fundamental in that it shows that the number of degrees of freedom decreases along the renormalization group flow. I will give a short history of and discuss recent developments in the quest to find its four-dimensional analogue using the central charges a & c.

There is an ongoing debate in the literature concerning the effects of averaging out inhomogeneities (``backreaction\'\') in cosmology. In particular, it has been suggested that the backreaction can play a significant role at late times, and that the standard perturbed FLRW framework is no longer a good approximation during structure formation, when the density contrast becomes nonlinear. After a brief introduction to the problem, I will show using Zalaletdinov\'s covariantaveraging scheme that as long as the metric of the universe can be described by the perturbed FLRW form, the corrections due to averaging remain negligibly small. Further, using a fully relativistic and reasonably generic model of pressureless spherical collapse, I will show that as long as matter velocities remain small (which is true in this model even at late times), the perturbed FLRW form of the metric can be explicitly recovered. Together with the observation that real peculiar velocities are in fact nonrelativistic, these results imply that the backreaction remains small even during nonlinear structure formation.