Finite domination and Novikov rings. Laurent polynomial rings in several variables

We present a homological characterisation of those chain complexes of modules over a Laurent polynomial ring in several indeterminates which are finitely dominated over the ground ring (that is, are a retract up to homotopy of a bounded complex of finitely generated free modules). The main tools, which we develop in the paper, are a non-standard totalisation construction for multi-complexes based on truncated products, and a high-dimensional mapping torus construction employing a theory of cubical diagrams that commute up to specified coherent homotopies.

Dynamics and structure of self-generated magnetics fields on solids following high contrast, high intensity laser irradiation

The dynamics of self-generated magnetic B-fields produced following the interaction of a high contrast, high intensity (I > 10¹⁹W cm^-2) laser beam with thin (3 μm thick) solid (Al or Au) targets is investigated experimentally and numerically. Two main sources drive the growth of B-fields on the target surfaces. B-fields are first driven by laser-generated hot electron currents that relax over ∼10-20 ps. Over longer timescales, the hydrodynamic expansion of the bulk of the target into vacuum also generates B-field induced by non-collinear gradients of density and temperature. The laser irradiation of the target front side strongly localizes the energy deposition at the target front, in contrast to the target rear side, which is heated by fast electrons over a much larger area. This induces an asymmetry in the hydrodynamic expansion between the front and rear target surfaces, and consequently the associated B-fields are found strongly asymmetric. The sole long-lasting (>30 ps) B-fields are the ones growing on the target front surface, where they remain of extremely high strength (∼8-10 MG). These B-fields have been recently put by us in practical use for focusing laser-accelerated protons [B. Albertazzi et al., Rev. Sci. Instrum. 86, 043502 (2015)]; here we analyze in detail their dynamics and structure.

Peace by Piece: (Re) imagining Division in Belfast’s Contested Spaces through Memory

This paper investigates processes and actions of diversifying memories of division in Northern Ireland’s political conflict known as the Troubles. Societal division is manifested in its built fabric and territories that have been adopted by predominant discourses of a fragmented society in Belfast; the unionist east and the nationalist west. The aim of the paper is to explore current approaches in planning contested spaces that have changed over time, leading to success in many cases. The argument is that divided cities, like Belfast, feature spatial images and memories of division that range from physical, clear-cut segregation to manifested actions of violence and have become influential representations in the community’s associative memory. While promoting notions of ‘re-imaging’ by current councils demonstrates a total erasure of the Troubles through cleansing its local collective memory, there yet remains an attempt to communicate a different tale of the city’s socio-economic past, to elaborate its supremacy for shaping future lived memories. Yet, planning Belfast’s contested areas is still suffering from a poor understanding of the context and its complexity against overambitious visions. 

Classifying Rational G-Spectra for Finite G

We give a new proof that for a finite group G, the category of rational G-equivariant spectra is Quillen equivalent to the product of the model categories of chain complexes of modules over the rational group ring of the Weyl group of H in G, as H runs over the conjugacy classes of subgroups of G. Furthermore, the Quillen equivalences of our proof are all symmetric monoidal. Thus we can understand categories of algebras or modules over a ring spectrum in terms of the algebraic model.

‘Ulster Says No’: Regulating the consumption of commercial sex spaces and services in Northern Ireland

Commercial forms of sex such as prostitution/sex work, strip clubs and even sex shops have been the subject of much political debate and policy regulation over the last decade or so in the UK and Ireland. These myriad forms of commercial sex and land usage have managed to survive and even thrive in the face of public outcry and regulation. Despite being part of the UK we suggest that Northern Ireland has steered its own regulatory course, whereby the consumption of commercial sexual spaces and services have been the subject of intense moral and legal oversight in ways that are not apparent in other UK regions. Nevertheless, in spite of this we also argue that the context of Northern Ireland may provide some lessons for the ways that religious values and moral reasoning can influence debates on commercial sex elsewhere.

Orbital and strongly orbital spaces

We say that a (countably dimensional) topological vector space X is orbital if there is T∈L(X) and a vector x∈X such that X is the linear span of the orbit {Tnx:n=0,1,…}. We say that X is strongly orbital if, additionally, x can be chosen to be a hypercyclic vector for T. Of course, X can be orbital only if the algebraic dimension of X is finite or infinite countable. We characterize orbital and strongly orbital metrizable locally convex spaces. We also show that every countably dimensional metrizable locally convex space X does not have the invariant subset property. That is, there is T∈L(X) such that every non-zero x∈X is a hypercyclic vector for T. Finally, assuming the Continuum Hypothesis, we construct a complete strongly orbital locally convex space.

As a byproduct of our constructions, we determine the number of isomorphism classes in the set of dense countably dimensional subspaces of any given separable infinite dimensional Fréchet space X. For instance, in X=ℓ2×ω, there are exactly 3 pairwise non-isomorphic (as topological vector spaces) dense countably dimensional subspaces.