Salem numbers and arithmetic hyperbolic groups

In this paper we prove that there is a direct relationship between Salem numbers and translation lengths of hyperbolic elements of arithmetic hyperbolic groups that are determined by a quadratic form over a totally real number field. As an application we determine a sharp lower bound for the length of a closed geodesic in a noncompact arithmetic hyperbolic n-orbifold for each dimension n. We also discuss a "short geodesic conjecture", and prove its equivalence with "Lehmer's conjecture" for Salem numbers.Comment: The exposition in version 3 is more compact; this shortens the paper: 26 pages now instead of 37. A discussion on Lehmer's problem has been added in Section 1.2. Final version, to appear is Trans. AM

In Better Fettle: Improvement, Work and Rhetoric in the Transition to Environmental Farming in the North York Moors

Through ethnographic research amongst farmers in the North York Moors, and through broader historical and political analysis, I examine the importance and role of values in hard work and beneficent change in negotiated interactions between policy-makers, farmers and conservationists. Within the context of a shift in agricultural support away from production to environmental protection, and within the context of a local conservation initiative to protect a population of freshwater pearl mussels in the River Esk, I show the importance of these values for the construction of farmers' personhoods and their symbolic relations and means of expression through the landscape. I show how those values are persistent and pervasive, yet at the same time mutable and open to interpretation. In particular, I examine alternative conceptions of beneficent change through recourse to the words fettle and improvement. Fettling places value in long-term, steady and incremental change, whereas improvement places value in changes more closely associated with productivist ideals such as expansion and profit. I suggest that it is the mutability of farming values that gives rise to their persistence as they come to be used and reinterpreted according to the changing contexts of their application and the differing interests of a range of groups and individuals. By showing that farmers are able to uphold and express their values differently I argue that it is not so straightforward to predict farmers' responses to changing political exigencies or local conservation initiatives on the basis of homogenous values or the categorisation of farmers into defined "types". Through a rhetoric-culture approach I argue that changes in farming values through time do not merely reflect changing political interests and farmers' subsequent accommodation of them. Rather, it reflects the continued negotiation of those values between farmers and others in the play of agents and patients in the construction of personhood and the formulation of arguments. I argue that the persistence of fettling interpretations of a value in beneficent change reflects the agentive actions of farmers as it remains a useful argumentative strategy with which they can make indictments against new policy impositions and, moreover, it remains functional in guiding their practices in ways suitable to the environment in which they farm

Quasi-1D dynamics and nematic phases in the 2D Emery model

We consider the Emery model of a Cu-O plane of the high temperature superconductors. We show that in a strong-coupling limit, with strong Coulomb repulsions between electrons on nearest-neighbor O sites, the electron-dynamics is strictly one dimensional, and consequently a number of asymptotically exact results can be obtained concerning the electronic structure. In particular, we show that a nematic phase, which spontaneously breaks the point- group symmetry of the square lattice, is stable at low enough temperatures and strong enough coupling.Comment: 8 pages, 5 eps figures; revised manuscript with more detailed discussions; two new figures and three edited figuresedited figures; 14 references; new appendix with a detailed proof of the one-dimensional dynamics of the system in the strong coupling limi

Performing inter-professional expertise in rural advisory networks

AbstractIn this paper we draw on in-depth research to explore inter-professional working in rural land and livestock management and introduce the novel concept of inter-professional expertise. An increasingly intricate regulatory framework, the diversification of the economic base of rural areas away from primary commodity production and a growing emphasis on environmental protection and ecosystem services mean that the management of land and livestock are becoming more complex in their objectives, more demanding of specialised technical knowledge and skills and more rule-bound in their procedures and processes. To assist them in meeting these challenges, farmers and other land managers turn to a growing array of rural professional advisers. Increasingly the achievement of private and public objectives for rural businesses depends upon the integration of a variety of specialised expert inputs. So, alongside pressures to differentiate the specialised knowledge they have to offer, rural professionals face demands to work together to help clients solve complex problems and deliver multiple objectives. It follows that rural land and livestock management present a rich context in which to explore the dynamic relationship between different types of professional experts. As a departure from the strong tradition of farmer-centred research examining extended knowledge networks in rural settings, we therefore explore the working relations between advisers themselves. Using concepts of relational agency and socio-material approaches we identify the skills and strategies involved in this inter-professional communication and working, with relevance to expert-expert interactions and the negotiation of contemporary professional expertise in fields far beyond the provision of rural services. We find that it is in the ways that experts perform, act and interact in the field that professional expertise and, by extension, inter-professional expertise – is realised and practised. Thus as working practices are increasingly shared, credentialism is pursued less by achieving the monopolies of old and more by striving for new monopolies of inter-professional practice

Quantum Theory of the Smectic Metal State in Stripe Phases

We present a theory of the electron smectic fixed point of the stripe phases of doped layered Mott insulators. We show that in the presence of a spin gap three phases generally arise: (a) a smectic superconductor, (b) an insulating stripe crystal and (c) a smectic metal. The latter phase is a stable two-dimensional anisotropic non-Fermi liquid. In the abscence of a spin gap there is also a more conventional Fermi-liquid-like phase. The smectic superconductor and smectic metal phases may have already been seen in Nd-doped LSCO.Comment: Brookhaven national Laboratory, University of Illinois at Urbana-Champaign, UCLA and University of Pennsylania; 4 pages, 2 figures, both figures are new. We have corrected the formuals for scaling dimensions (eq. 4) and the discussion that follows from it. The figures have been redrwa