Jet measurements in pp, p--Pb and Pb--Pb collisions with ALICE at the LHC

We present a systematic study of jet measurements in pp, p--Pb and Pb--Pb collisions using the ALICE detector at the LHC. Jet production cross sections are measured in pp collisions at $\sqrt{s}$ = 2.76 and 7~TeV, in p--Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02~TeV and in Pb--Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76~TeV. Jet shape observables and fragmentation distributions are measured in pp collisions at 7~TeV. Jets are reconstructed at midrapidity in a wide range of transverse momentum using sequential recombination jet finding algorithms ($k_{\rm T}$, anti-$k_{\rm T}$, and SISCone) with several values of jet resolution parameter $R$ in the range 0.2 -- 0.6. Measurements are compared to Next-to-Leading Order (NLO) perturbative Quantum Chromodynamics (pQCD) calculations and predictions from Monte Carlo (MC) event generators such as PYTHIA, PHOJET and HERWIG. Jet production cross sections are well reproduced by NLO pQCD calculations in pp collisions at $\sqrt{s}$~=~2.76~TeV. MC models could not explain the jet cross sections in pp collisions at $\sqrt{s}$ = 7 TeV, whereas jet shapes and fragmentation distributions are rather well reproduced by these models. The jet nuclear modification factor $R_{\rm pPb}$ in p--Pb collisions is found to be consistent with unity indicating the absence of large modifications of the initial parton distribution or strong final state effects on jet production, whereas a large jet suppression is observed in Pb--Pb central events with respect to peripheral events indicating formation of a dense medium in central Pb--Pb events.Comment: 6 pages, 5 figures, 7th International Conference on Physics and Astrophysics of Quark Gluon Plasma, 1-5 February, 2015, Kolkata, Indi

Wage Inequality in the United Kingdom, 1975-99

U.K. cross-sectional wage inequality rose sharply in the 1980s, continued to rise moderately through the mid-1990s, and has remained essentially unchanged since then. As in the U.S., increases in within-group inequality account for a substantial fraction of the rise in wage dispersion during the period 1975-99. Compositional shifts in the occupational and industry structures of aggregate employment also had important effects on the evolution of wage inequality. The convergence of the wage distributions for men and women has, however, had a stabilizing effect on the overall wage distribution. Copyright 2002, International Monetary Fund

Local-global principles for embedding of fields with involution into simple algebras with involution

In this paper we prove local-global principles for embedding of fields with involution into central simple algebras with involution over a global field. These should be of interest in study of classical groups over global fields. We deduce from our results that in a group of type D_n, n>4 even, two weakly commensurable Zariski-dense S-arithmetic subgroups are actually commensurable. A consequence of this result is that given an absolutely simple algebraic K-group G of type D_n, n>4 even, K a number field, any K-form G' of G having the same set of isomorphism classes of maximal K-tori as G, is necessarily K-isomorphic to G. These results lead to results about isolength and isospectral compact hyperbolic spaces of dimension 2n-1 with n even

On the fields generated by the lengths of closed geodesics in locally symmetric spaces

This paper is the next installment of our analysis of length-commensurable locally symmetric spaces begun in Publ. math. IHES 109(2009), 113-184. For a Riemannian manifold $M$, we let $L(M)$ be the weak length spectrum of $M$, i.e. the set of lengths of all closed geodesics in $M$, and let $\mathcal{F}(M)$ denote the subfield of $\mathbb{R}$ generated by $L(M)$. Let now $M_i$ be an arithmetically defined locally symmetric space associated with a simple algebraic $\mathbb{R}$-group $G_i$ for $i = 1, 2$. Assuming Schanuel's conjecture from transcendental number theory, we prove (under some minor technical restrictions) the following dichotomy: either $M_1$ and $M_2$ are length-commensurable, i.e. $\mathbb{Q} \cdot L(M_1) = \mathbb{Q} \cdot L(M_2)$, or the compositum $\mathcal{F}(M_1)\mathcal{F}(M_2)$ has infinite transcendence degree over $\mathcal{F}(M_i)$ for at least one $i = 1$ or $2$ (which means that the sets $L(M_1)$ and $L(M_2)$ are very different)

Generic elements in Zariski-dense subgroups and isospectral locally symmetric spaces

The article contains a survey of results on length-commensurable and isospectral locally symmetric spaces and related problems in the theory of semi-simple algebraic groups.Comment: New material has been added in section