Three-dimensional quantum geometry and black holes

We review some aspects of three-dimensional quantum gravity with emphasis in the `CFT -> Geometry' map that follows from the Brown-Henneaux conformal algebra. The general solution to the classical equations of motion with anti-de Sitter boundary conditions is displayed. This solution is parametrized by two functions which become Virasoro operators after quantisation. A map from the space of states to the space of classical solutions is exhibited. Some recent proposals to understand the Bekenstein-Hawking entropy are reviewed in this context. The origin of the boundary degrees of freedom arising in 2+1 gravity is analysed in detail using a Hamiltonian Chern-Simons formalism.Comment: 39 pages, Latex, no figures. Invited talk at the Second Meeting "Trends in Theoretical Physics", held in Buenos Aires, December, 1998. v2: References added and minor corrections. v3: An incorrect statement about the sign of the Chern-Simons level erased. Extended (and in some cases modified) discussions in most sections. References adde

Notes on black holes and three dimensional gravity

These notes are the written version of two lectures delivered at the VIII Mexican School on Particles and Fields on November 1998. The level of the notes is basic assuming only some knowledge on Statistical Mechanics, General Relativity and Yang-Mills theory. After a brief introduction to the classical and semiclassical aspects of black holes, we review some relevant results on 2+1 quantum gravity. These include the Chern-Simons formulation and its affine Kac-Moody algebra, the asymptotic algebra of Brown and Henneaux, and the statistical mechanics description of 2+1 black holes. Hopefully, this contribution will be complementary with the review paper hep-th/9901148 by the same author, and perhaps, a shortcut to some recent developments in three dimensional gravity.Comment: 20 pages. Uses aipproc. To appear in the proceedings of the VIII Mexican School on Particles and Field

Analyzing the Spillover Mechanism on the Semiconductor Industry in the Silicon Valley and Route 128

To understand the impact of science and engineering innovations on economic growth requires relating discoveries to products, and identifying the scientists and engineers who are responsible for the knowledge transfer. Studies reliant on geographic proximity alone can show only that economic activity varies positively with the amount of research being done at a university [David (1992), Nelson and Romer (1996), Jaffe (1989,93)]. These "geographically localized knowledge spillovers" have proved unable to explain what it is about research universities that is crucial for their local economic impact (training, the research findings?) and, therefore, are unconvincing both to policy makers and the public. This paper analyses the spillover mechanism identifying its main components by analyzing the effect of university-based star scientists through explicit and implicit ties, and the effect of other neighbor firms, on the performance of semiconductor enterprises measured with patents. Explicit ties are modeled by the full and part-time job mobility of scientists located in universities; and implicit ties, by the presence of positive externalities or spillover effects to the firms of untied scientists at Universities in the same economic area. Specifically, this study examines the Silicon Valley and Route 128 cases in detail identifying the differences and similarities between these two major semiconductor regions in their spillover mechanisms. Previous research on high-technology industries has demonstrated the importance of geographically localized "knowledge spillovers" by building specific links between university scientists and firms and estimating the local effects of different types of links. This research goes an step forward, by not only measuring the effect of University research through the direct ties to firms (Zucker, Darby, Armstrong; 1998); but also measuring the importance of the inside industry R&D spillovers in the growth of the region.