We discuss the possible phases dual to the AdS hairy black holes in Horndeski theory. In the probe limit breaking the translational invariance, we study the conductivity and we find a non-trivial structure indicating a collective excitation of the charge carriers. Going beyond the probe limit, we investigate the spontaneous breaking of translational invariance near the critical temperature and discuss the stability of the theory. We consider the backreaction of the charged scalar field to the metric and we construct numerically the hairy black hole solution. To determine the dual phases of a hairy black hole, we compute the conductivity. When the wave number of the scalar field is zero, the DC conductivity is divergent due to the conservation of translational invariance. For nonzero wave parameter with finite DC conductivity, we find two phases in the dual theory. For low temperatures and for positive couplings, as the temperature is lower, the DC conductivity increases therefore the dual theory is in metal phase, while if the coupling is negative we have the opposite behavior and it is dual to an insulating phase. We argue that this behavior of the coupling of the scalar field to Einstein tensor can be attributed to its role as an impurity parameter in the dual theory.

*Local: Sala Jayme Tiomno*

Dark matter is an indispensable component to explain the large scale structure of the universe. However, some theoretical expectations are still in contradiction with observations as, for instance, the large number of predicted satellites, the central mass distribution of galaxies, the presence of massive galaxies and clusters at redshift z > 2. Moreover, LHC data do not indicate detection of supersymmetric particles, posing problems to the nature of dark matter. I will discuss an alternative scenario in which dark matter particles are primordial extreme regular black holes formed at the end of inflation, during the reheating era.

Local: Sala Jayme Tyomno

Riemann hypothesized that the zeta function ζ(s) has (non-trivial) zeroes only on the line Re(s) = 1/2 in the complex s-plane. Hilbert and Polya suggested that the position of these zeroes might be related to the spectrum of a `Hamiltonian'. It has been known for some time that the statistical properties of the eigenvalue distribution of an ensemble of random matrices resemble those of the zeroes of the zeta function. We construct a unitary matrix models (UMM) for the zeta function, however, our approach to the problem is `piecemeal'. That is, we consider each factor in the Euler product representation of the zeta function to get a UMM for each prime. This suggests a Hamiltonian (of the type proposed by Berry and Keating) from its phase space description. We attempt to combine this to get a matrix model for the full zeta function.

Local: Sala Jayme Tiomno

Descreverei, de maneira não técnica, resultados que obtive com diversos co-autores nos últimos anos, explorando a ideia de que modelos ferromagnéticos, quando na presença de campos externos, podem ter o comportamento do mesmo modelo com campo nulo ou com campo uniforme não-nulo, dependendo da velocidade com que este decai a zero. O exemplos são modelos de Ising na rede e em árvores, e, também, modelos de Dyson na rede unidimensional Z. Neste último caso, obtemos o primeiro exemplo de uma medida de Gibbs que não é uma g-medida.

Local: Sala Jayme Tiomno