Talks

I will discuss a holographic model whose low-energy physics may be used to build a marginal Fermi liquid. The model has several interesting features, including (i.) it is embedded in string theory and we possess a Lagrangian description of the field theory, (ii.) it exhibits a first-order transition between the non-Fermi liquid phase and a normal Fermi liquid phase, and (iii.) the model involves a lattice of heavy defects interacting with a sea of propagating fields.

Various self-similar spherically symmetric spacetimes admit naked singularities, providing a challenge to the cosmic censorship hypothesis. However, it is not clear if the naked singularities are artefacts of the high degree of symmetry of the spacetimes, or if they are potentially generically present. To address this question, we consider perturbations of (various cases of) these spacetimes, focusing particularly on the behaviour of the perturbations as they impinge on the Cauchy horizon. We describe recent results on self-similar Lemaitre-Tolman-Bondi spacetime, indicating stability of scalar and odd parity perturbations, and instability of even parity perturbations.

A symmetric informationally complete positive-operator-valued measure (SIC POVM) is a special POVM that is composed of d^2 subnormalized pure projectors with equal pairwise fidelity. It may be considered a fiducial POVM for reasons of its high symmetry and high tomographic efficiency. Most known SIC POVMs are covariant with respect to the Heisenberg-Weyl (HW) group. We show that in prime dimensions the HW group is the unique group that may generate a SIC POVM. In particular, in prime dimensions not equal to three, each group covariant SIC POVM is covariant with respect to a unique HW group. In addition, the symmetry group of the SIC POVM is a subgroup of the Clifford group, which is the normalizer of the HW group. Hence, two SIC POVMs covariant with respect to the HW group are unitarily equivalent if and only if they are on the same orbit of the Clifford group. In dimension three, each group covariant SIC POVM may be covariant with respect to three or nine HW groups, and the symmetry group of the SIC POVM is a subgroup of at least one of the Clifford groups of these HW groups respectively. There may exist two or three orbits of equivalent SIC POVMs for each group covariant SIC POVM, depending on the order of its symmetry group.