Holomorphic curves in exploded manifolds: regularity

The category of exploded manifolds is an extension of the category of smooth manifolds related to tropical geometry in which some adiabatic limits appear as smooth families. This paper studies the dbar equation on variations of a given family of curves in an exploded manifold. Roughly, we prove that the dbar equation on variations of an exploded family of curves behaves as nicely as the dbar equation on variations of a smooth family of smooth curves, even though exploded families of curves allow the development of normal crossing or log smooth singularities. The resulting regularity results are used in a series of separate papers to construct Gromov Witten invariants for exploded manifolds.Comment: 52 pages. v2: The construction of Gromov Witten invariants has been removed to another paper. v3: rewritten introduction, improved exposition. v4, v5: improved exposition v6, v7: Minor improvements and some expanded explanations, (including weakened hypothesis for Proposition 3.11), as suggested by an anonymous referee of a different paper. Final version to appear in Geometry and Topolog

Particle creation and particle number in an expanding universe

I describe the logical basis of the method that I developed in 1962 and 1963 to define a quantum operator corresponding to the observable particle number of a quantized free scalar field in a spatially-flat isotropically expanding (and/or contracting) universe. This work also showed for the first time that particles were created from the vacuum by the curved space-time of an expanding spatially-flat FLRW universe. The same process is responsible for creating the nearly scale-invariant spectrum of quantized perturbations of the inflaton scalar field during the inflationary stage of the expansion of the universe. I explain how the method that I used to obtain the observable particle number operator involved adiabatic invariance of the particle number (hence, the name adiabatic regularization) and the quantum theory of measurement of particle number in an expanding universe. I also show how I was led in a surprising way, to the discovery in 1964 that there would be no particle creation by these spatially-flat FLRW universes for free fields of any integer or half-integer spin satisfying field equations that are invariant under conformal transformations of the metric. The methods I used to define adiabatic regularization for particle number, were based on generally-covariant concepts like adiabatic invariance and measurement that were fundamental and determined results that were unique to each given adiabatic order.Comment: 22 pages, no figures, submitted 7May2012 to J. Phys. A for a special issue honoring Prof. Stuart Dowke

Core groups and the transmission of HIV: Learning from male sex workers

A growing and substantial body of research suggests that female sex workers play a disproportionately large role in the transmission of HIV in many parts of the world, and they are often referred to as core groups by epidemiologists, mathematical modellers, clinicians and policymakers. Male sex workers, by contrast, have received little attention and it is not known whether it is helpful to conceptualize them as a core group. This paper draws upon ethnographic research documenting social and sexual networks in London and looks at the position of five male sex workers within a network comprising 193 men and seven women (as well as 1378 anonymous sexual contacts and 780 commercial contacts). In so doing, it suggests that there is no evidence to show that male sex workers are more or less likely to acquire or transmit HIV in the course of commercial sex compared with other types of sexual relationships. In addition, men engaging in non-commercial sex all reported having unprotected sex in a variety of contexts and relationships and there is no evidence to suggest that men who are not sex workers play less of a role in the transmission of HIV. In short, these data suggest that it would be inappropriate to conceptualize male sex workers as a core group. This is not to suggest that public policy should continue to overlook male sex workers. New and inventive approaches are required to reach out to a vulnerable but diverse group of men, selling sex for a variety of reasons; even if these men are no more vulnerable to acquiring and/or transmitting HIV than other men and women that form part of their network