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In this talk I will summarise the recent progress in AdS/CFT due to the construction of the new infinite family of Sasaki-Einstein metrics Y^{p,q}, and their dual superconformal gauge theories. I will review some aspects of Sasaki-Einstein geometry and the main features of the Y^{p,q} metrics. I will then discuss the use of toric geometry to obtain a description of the corresponding Y^{p,q} Calabi-Yau singularities. I will explain how the AdS/CFT dual N=1 supersymmetric gauge theories were constructed using the combined information obtained from the metrics and the toric singularities. A crucial check on the consistency of the construction is provided by the field theory technique of a-maximisation. In the last part of the talk I will briefly discuss the recently formulated geometric dual of this, i.e. "Z-minimisation".

A key issue in the context of (compact) extra dimensions is the one of their stability. Any stabilization mechanism is effective only up to some given energy scale; if they can approach this energy, 4$d observers can excite the fluctuations of the internal space, and probe its existence. Stabilization mechanisms introduce fields in the internal space; perturbations of these fields are mixed with perturbations of the metric, so that their study requires a complete GR treatment. After presenting the general framework, I will then discuss some relevant applications. I will present the exact coupling of the radion to codimension one branes, extending the regime of validity of the results in the literature. I will then focus on de Sitter compactifications, showing that the cosmological expansion has typically the effect of destabilizing the internal space. The final part of the talk will be devoted to related work in progress in less conventional areas of brane models: the localization of gravity towards the IR brane (corresponding to a dual description of emerging gravity from the CFT), and the inclusion of ghost fields in the bulk.

Since the seminal discovery of the neutrino by Cowan and Reines in the late 1950's, intense experimental and theoretical effort has focused on the elucidation of neutrino properties and the role they play in elementary particle physics, astrophysics, and cosmology. Neutrinos are born in the fusion reactions powering our Sun and are thought to be the driving mechanism for supernova explosions. Neutrinos exist in copious amounts as the primordial afterglow of the Big Bang and, if massive, would play a role in the evolution and ultimate fate of the Universe. Central to many of the key issues in neutrino physics is the question of whether neutrinos possess non-zero rest mass. If neutrinos are massive, then one expects flavor mixing to occur in the neutrino sector which could lead to the phenomena of neutrino oscillations and the possibility of CP violation in the neutrino sector. A detailed understanding of the microscopic properties of neutrinos can serve to pave the way to a unified description of the fundamental forces of Nature.

In this talk we assume that Quantum Einstein Gravity (QEG) is the correct theory of gravity on all length scales. We use both analytical results from nonperturbative renormalization group (RG) equations and experimental input in order to describe the special RG trajectory of QEG which is realized in Nature. We identify a regime of scales where gravitational physics is well described by classical General Relativity. Strong renormalization effects occur at both larger and smaller momentum scales. The former are related to the (conjectured) nonperturbative renormalizability of QEG. The latter lead to a growth of Newton's constant at large distances. We argue that this effect becomes visible at the scale of galaxies and could provide a solution to the astrophysical missing mass problem which does not require dark matter. A possible resolution of the cosmological constant problem is proposed by noting that all RG trajectories admitting a long classical regime automatically imply a small cosmological constant.

The existence, and enigmatic nature, of 'Dark Energy' is one of the biggest theoretical upsets of recent times. In this seminar we present ideas on alternative theoretical and phenomenological approaches to the Dark Energy problem, in particular the issue of whether dark energy is a matter or gravity-based phenomenon, and the ways in which such approaches can been constrained and guided by observation. We also focus on some of the exciting future approaches that could provide unprecedented insights into the fundamentals of Dark Energy