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More than forty years ago Nobel laureate P.W. Anderson studied the overlap between two nearby ground states. The result that the overlap tends to zero in the thermodynamics limit was catastrophic for those times. More recently the study of the overlap between ground states, i.e. the fidelity, led to the formulation of the so called fidelity approach to (quantum) phase transition (QPT). This new approach to QPT does not rely on the identification of order parameters or symmetry pattern; rathers it embodies the theory of phase transitions with an operational meaning in terms of measurements. Nowadays orthogonality of ground states is much less surprising. I will provide the general scaling behavior of the fidelity at regular and at critical points of the phase diagrams, Anderson's result being a particular case. These results are useful to many areas of theoretical physics. A related quantity extensively studied here, the fidelity susceptibility, is well known in various other contexts under different names. In metrology it is called quantum Fisher information; in the theory of adiabatic computation it represents the figure of merit for efficient computation; in yet another context it is known as (real part of) the Berry geometric tensor.

Theories with extra dimensions naturally give rise to a large landscape of vacua stabilized by flux. I will show that the fastest decay is a giant leap to a wildly distant minimum, in which many different fluxes discharge at once. Indeed, the fastest decay is frequently the giantest leap of all, where all the fluxes discharge at once, which destabilizes the extra dimensions and begets a bubble of nothing. Finally, I will discuss how these giant leaps are mediated by the nucleation of "monkey branes" that wrap the extra dimensions.

We will discuss two topics. First we will revisit the asymptotic structure of classical de Sitter space. In particular we will construct charges at future infinity (I^+) and obtain the asymptotic symmetry group drawing parallels with the BMS group of flat space. Secondly, move away from the region I^+ and study the space living near the cosmological horizon by considering large rotating Nariai black holes whose size tends to that of the cosmological horizon. We will examine the resulting near (cosmological) horizon geometry and find an interesting asymptotic structure containing the Virasoro algebra, suggestive of a holographic interpretation.

A picture can be used to represent an experiment. In this talk we will consider such pictures and show how to turn them into pictures representing calculations (in the style of Penrose's diagrammatic tensor notation). In particular, we will consider circuits described probabilistically. A circuit represents an experiment where we act on various systems with boxes, these boxes being connected by the passage of systems between them. We will make two assumptions concerning such circuits. These two assumptions allow us to set up the duotensor framework (a duotensor is like a tensor except that each position is associated with two possible bases). We will see that quantum theory can be formulated in this framework. Each of the usual objects of quantum theory (states, measurements, transformations) are special cases of duotensors. The framework is motivated by the objective of providing a formulation of quantum theory which is local in the sense that, in doing a calculation pertaining to a particular region of spacetime, we need only use mathematical objects that pertain to this same region. This is, I argue, a prerequisite in a theory of quantum gravity. Reference for this talk: http://arxiv.org/abs/1005.5164