Abstract:
Using symmetric space techniques, we show that closed orbits of the Iwasawa subgroups of $SO(2,l-1)$ naturally define singularities of a black hole causal structure in anti-de Sitter spaces in $l \geq 3$ dimensions. In particular, we recover for $l=3$ the non-rotating massive BTZ black hole. The method presented here is very simple and in principle generalizable to any semi-simple symmetric space.

Abstract:
We propose a set of consistent boundary conditions containing the spacelike warped black holes solutions of Topologically Massive Gravity. We prove that the corresponding asymptotic charges whose algebra consists in a Virasoro algebra and a current algebra are finite, integrable and conserved. A similar analysis is performed for the timelike warped AdS_3 spaces which contain a family of regular solitons. The energy of the boundary Virasoro excitations is positive while the current algebra leads to negative (for the spacelike warped case) and positive (for the timelike warped case) energy boundary excitations. We discuss the relationship with the Brown-Henneaux boundary conditions.

Abstract:
We describe the space of (all) invariant deformation quantizations on the hyperbolic plane as solutions of the evolution of a second order hyperbolic differential operator. The construction is entirely explicit and relies on non-commutative harmonic analytical techniques on symplectic symmetric spaces. The present work presents a unified method producing every quantization of the hyperbolic plane, and provides, in the 2-dimensional context, an exact solution to Weinstein's WKB quantization program within geometric terms. The construction reveals the existence of a metric of Lorentz signature canonically attached (or `dual') to the geometry of the hyperbolic plane through the quantization process.

Abstract:
It is shown that the warped black holes geometries discussed recently in 0807.3040 admit an algebra of asymptotic symmetries isomorphic to the semi-direct product of a Virasoro algebra and an algebra of currents. The realization of this asymptotic symmetry by canonical charges allows one to find the central charge of the Virasoro algebra. The right-moving central charge $c_R = \frac{(5\hat{\nu}^2+3)l}{G\hat{\nu} (\hat{\nu}^2+3)}$ is obtained when the Virasoro generators are normalized in order to have a positive zero mode spectrum for the warped black holes. The current algebra is also shown to be centrally-extended.

Abstract:
We analyze the asymptotic solutions of Chiral Gravity (Topologically Massive Gravity at \mu l = 1 with Brown-Henneaux boundary conditions) focusing on non-Einstein metrics. A class of such solutions admits curvature singularities in the interior which are reflected as singularities or infinite bulk energy of the corresponding linear solutions. A non-linear solution is found exactly. The back-reaction induces a repulsion of geodesics and a shielding of the singularity by an event horizon but also introduces closed timelike curves.

Abstract:
We discuss the asymptotic symmetry algebra of the Schrodinger-invariant metrics in d+3 dimensions and its realization on finite temperature solutions of gravity coupled to matter fields. These solutions have been proposed as gravity backgrounds dual to non-relativistic CFTs with critical exponent z in d space dimensions. It is known that the Schrodinger algebra possesses an infinite-dimensional extension, the Schrodinger-Virasoro algebra. However, we show that the asymptotic symmetry algebra of Schrodinger spacetimes is only isomorphic to the exact symmetry group of the background. It is possible to construct from first principles finite and integrable charges that infinite-dimensionally extend the Schrodinger algebra but these charges are not correctly represented via a Dirac bracket. We briefly comment on the extension of our analysis to spacetimes with Lifshitz symmetry.

Abstract:
We initiate a comprehensive study of a set of solutions of topologically massive gravity known as null warped anti-de Sitter spacetimes. These are pp-wave extensions of three-dimensional anti-de Sitter space. We first perform a careful analysis of the linearized stability of black holes in these spacetimes. We find two qualitatively different types of solutions to the linearized equations of motion: the first set has an exponential time dependence, the second - a polynomial time dependence. The solutions polynomial in time induce severe pathologies and moreover survive at the non-linear level. In order to make sense of these geometries, it is thus crucial to impose appropriate boundary conditions. We argue that there exists a consistent set of boundary conditions that allows us to reject the above pathological modes from the physical spectrum. The asymptotic symmetry group associated to these boundary conditions consists of a centrally-extended Virasoro algebra. Using this central charge we can account for the entropy of the black holes via Cardy's formula. Finally, we note that the black hole spectrum is chiral and prove a Birkoff theorem showing that there are no other stationary axisymmetric black holes with the specified asymptotics. We extend most of the analysis to a larger family of pp-wave black holes which are related to Schr\"odinger spacetimes with critical exponent z.

Abstract:
We consider zero-sum stochastic games with finite state and action spaces, perfect information, mean payoff criteria, without any irreducibility assumption on the Markov chains associated to strategies (multichain games). The value of such a game can be characterized by a system of nonlinear equations, involving the mean payoff vector and an auxiliary vector (relative value or bias). We develop here a policy iteration algorithm for zero-sum stochastic games with mean payoff, following an idea of two of the authors (Cochet-Terrasson and Gaubert, C. R. Math. Acad. Sci. Paris, 2006). The algorithm relies on a notion of nonlinear spectral projection (Akian and Gaubert, Nonlinear Analysis TMA, 2003), which is analogous to the notion of reduction of super-harmonic functions in linear potential theory. To avoid cycling, at each degenerate iteration (in which the mean payoff vector is not improved), the new relative value is obtained by reducing the earlier one. We show that the sequence of values and relative values satisfies a lexicographical monotonicity property, which implies that the algorithm does terminate. We illustrate the algorithm by a mean-payoff version of Richman games (stochastic tug-of-war or discrete infinity Laplacian type equation), in which degenerate iterations are frequent. We report numerical experiments on large scale instances, arising from the latter games, as well as from monotone discretizations of a mean-payoff pursuit-evasion deterministic differential game.

We consider general regime switching stochastic volatility models where both the asset and the volatility dynamics depend on the values of a Markov jump process. Due to the stochastic volatility and the Markov regime switching, this financial market is thus incomplete and perfect pricing and hedging of options are not possible. Thus, we are interested in finding formulae to solve the problem of pricing and hedging options in this framework. For this, we use the local risk minimization approach to obtain pricing and hedging formulae based on solving a system of partial differential equations. Then we get also formulae to price volatility and variance swap options on these general regime switching stochastic volatility models.

This research paper aims to study the correlation between the port activity and the activity of the different services sectors. By comparing trends between them and analyzing the causality relationships between the port traffic and the other economic sectors, our study tends to present how the activity of the port of Abidjan could have a decisive effect on the local economy. To meet our objectives, correlation analysis and statistical test tools Eviews and other techniques have been run with data provided by local agencies and port authority. By doing so, our research study finds that there is existing correlation between port activity and activity generated by the other services sectors and its contribution can accelerate the economic growth.