LAPACK-Based Software for Subspace Identification

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New Loop Representations for 2+1 Gravity

Since the gauge group underlying 2+1-dimensional general relativity is non-compact, certain difficulties arise in the passage from the connection to the loop representations. It is shown that these problems can be handled by appropriately choosing the measure that features in the definition of the loop transform. Thus, ``old-fashioned'' loop representations - based on ordinary loops - do exist. In the case when the spatial topology is that of a two-torus, these can be constructed explicitly; {\it all} quantum states can be represented as functions of (homotopy classes of) loops and the scalar product and the action of the basic observables can be given directly in terms of loops.Comment: 28pp, 1 figure (postscript, compressed and uuencoded), TeX, Pennsylvania State University, CGPG-94/5-

The Formation and Growth of the Earliest Supermassive Black Holes

Understanding how supermassive black holes (BHs) form and grow in the very early (z>6) Universe, when the first stars and galaxies were forming, is one of the major science aims of the Athena mission. The physical processes responsible for the initial formation of these BHs and their early growth via accretion - when they are seen as Active Galactic Nuclei (AGNs) - remain unclear. Large-scale optical/near-infrared imaging surveys have identified a few tens of luminous AGNs at z>6, powered by extremely massive BHs, and place vital constraints on the range of possible formation and growth mechanisms. To make further progress, however, we must identify lower luminosity and obscured AGNs at z>6, which represent the bulk of early BH growth. I will discuss recent measurements that trace the evolution of AGN population out to the highest possible redshifts (z~5-6) using the latest X-ray surveys with Chandra and XMM-Newton. However, Athena will provide the superb sensitivity over a wide field-of-view that is required to identify the earliest (z>6) growing BHs, trace their evolution within the early galaxy population, and determine the physical mechanisms that drive their formation and growth. Achieving these aims represents a major challenge that will push the capabilities of both Athena and supporting ground- and space-based observatories. I will present the prospects for a large Athena survey programme and discuss both the technical and scientific challenges that must be addressed in preparation for the Athena mission. <P /