Higgs bundles and higher Teichm\"uller spaces

This paper is a survey on the role of Higgs bundle theory in the study of higher Teichm\"uller spaces. Recall that the Teichm\"uller space of a compact surface can be identified with a certain connected component of the moduli space of representations of the fundamental group of the surface into $\mathrm{PSL}(2,{\mathbb{R}})$. Higher Teichm\"uller spaces correspond to special components of the moduli space of representations when one replaces $\mathrm{PSL}(2,{\mathbb{R}})$ by a real non-compact semisimple Lie group of higher rank. Examples of these spaces are provided by the Hitchin components for split real groups, and maximal Toledo invariant components for groups of Hermitian type. More recently, the existence of such components has been proved for $\mathrm{SO}(p,q)$, in agreement with the conjecture of Guichard and Wienhard relating the existence of higher Teichm\"uller spaces to a certain notion of positivity on a Lie group that they have introduced. We review these three different situations, and end up explaining briefly the conjectural general picture from the point of view of Higgs bundle theory.Comment: arXiv admin note: substantial text overlap with arXiv:1511.0775

The evolution of retail in Romania

The past years have brought important changes into the Romanian retail sector. The changes started to rush after the moment when Romania was becoming a member of the European Union, was a fact. The various researches which have been made in the retail domain reveal the development of the new ways of trading, leaving the traditional trading one step behind. Through this debate I intend to bring out a picture concerning the evolution of “retail“ in the last years in Romania, to outline the retail sector at this moment and eventually to anticipate the tendencies which will be present in the Romanian retail sector in perspective. The last years have brought especially important changes in the retail sector in Romania. The changes began to more obviously manifest after Romania’s adhesion became a certainty. The results from numerous researches in retail reveal the evolution of new types of commerce in the detriment of those represented by traditional commerce and implicitly the change in the structure of the local retail. Trough this paper I seek to portray an x-ray of the evolution of retail in Romania of the last years, to underline the retails’ sector actual state, also to anticipate the tendencies that will manifest in the Romanian retail sector in the near future.retail, hypermarket, supermarket, cash&carry

Redshift remapping and cosmic acceleration in dark-matter-dominated cosmological models

The standard relation between the cosmological redshift and cosmic scale factor underlies cosmological inference from virtually all kinds of cosmological observations, leading to the emergence of the LambdaCDM cosmological model. This relation is not a fundamental theory and thus observational determination of this function (redshift remapping) should be regarded as an insightful alternative to holding its standard form in analyses of cosmological data. Here we present non-parametric reconstructions of redshift remapping in dark-matter-dominated models and constraints on cosmological parameters from a joint analysis of all primary cosmological probes including the local measurement of the Hubble constant, Type Ia supernovae, baryonic acoustic oscillations (BAO), Planck observations of the cosmic microwave background (CMB) radiation (temperature power spectrum) and cosmic chronometers. The reconstructed redshift remapping points to an additional boost of redshift operating in late epoch of cosmic evolution, but affecting both low-redshift observations and the CMB. The model predicts a significant difference between the actual Hubble constant, h=0.48+/-0.02, and its local determination, h_obs=0.73+/-0.02. The ratio of these two values coincides closely with the maximum expansion rate inside voids formed in the corresponding open cosmological model with Omega_m=0.87+/-0.03, whereas the actual value of the Hubble constant implies the age of the Universe that is compatible with the Planck LambdaCDM cosmology. The new dark-matter-dominated model with redshift remapping provides excellent fits to all data and eliminates recently reported tensions between the Planck LambdaCDM cosmology, the local determination of the Hubble constant and the BAO measurements from the Ly-alpha forest of high-redshift quasars.Comment: 21 pages, 11 figures, 4 tables; accepted for publication in MNRA

New Parametrizations of Non-Gaussian Line-of-sight Velocity Distribution

A five-parameter fitting formula for the line-of-sight stellar velocity distributions of steady state systems is proposed. It can faithfully reproduce velocity distributions of theoretical models ranging from nearly Gaussian profiles to strongly skewed or mildly double-peaked profiles. In contrast to van der Marel and Franx (1993) and Kuijken and Merrifield (1993), the line profiles are required to have neither multi-peaks nor negative velocity wings. Information of the profile is mostly specified by five physically meaningful and nearly orthogonal fitting parameters.Comment: submitted to MNRAS; 22 pages with 3 tables and 8 figures in uuencoded compressed PS file. Also available at ftp://ibm-1.mpa-garching.mpg.de/pub/hsz/profile.u

Effects of long-wavelength fluctuations in large galaxy surveys

In order to capture as much information as possible large galaxy surveys have been increasing their volume and redshift depth. To face this challenge theory has responded by making cosmological simulations of huge computational volumes with equally increasing the number of dark matter particles and supercomputing resources. Thus, it is taken for granted that the ideal situation is when a single computational box encompasses the whole effective volume of the observational survey, e.g., ~50 Gpch^3 for the DESI and Euclid surveys. Here we study the effects of missing long-waves in a finite volume using several relevant statistics: the abundance of dark matter halos, the PDF, the correlation function and power spectrum, and covariance matrices. Finite volume effects can substantially modify the results if the computational volumes are less than ~(500Mpch)^3. However, the effects become extremely small and practically can be ignored when the box-size exceeds ~1Gpch^3. We find that the average power spectra of dark matter fluctuations show remarkable lack of dependence on the computational box-size with less than 0.1% differences between 1Gpch and 4Gpch boxes. No measurable differences are expected for the halo mass functions for these volumes. The covariance matrices are scaled trivially with volume, and small corrections due to super-sample modes can be added. We conclude that there is no need to make those extremely large simulations when a box-size of 1-1.5Gpch is sufficient to fulfil most of the survey science requirements.Comment: 15 pages, 14 figures, accepted to MNRA