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Hamilton's Ricci flow has attracted considerable attention since its introduction in 1982, owing partly to its promise in addressing the Poincaré conjecture and Thurston's geometrization conjecture. This book gives a concise introduction to the subject with the hindsight of Perelman's breakthroughs from 2002/2003. After describing the basic properties of, and intuition behind the Ricci flow, core elements of the theory are discussed such as consequences of various forms of maximum principle, issues related to existence theory, and basic properties of singularities in the flow. A detailed exposition of Perelman's entropy functionals is combined with a description of Cheeger-Gromov-Hamilton compactness of manifolds and flows to show how a 'tangent' flow can be extracted from a singular Ricci flow. Finally, all these threads are pulled together to give a modern proof of Hamilton's theorem that a closed three-dimensional manifold whichcarries a metric of positive Ricci curvature is a spherical space form.

Ricci flow. --- Flow, Ricci --- Evolution equations --- Global differential geometry

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Excavations (Archaeology) --- Neolithic period --- Landscape archaeology --- Fouilles (Archéologie) --- Néolithique --- Archéologie du paysage --- Congresses. --- Congrès --- Europe --- Antiquities --- Antiquités

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This new title in the acclaimed Prehistoric Society Research Papers series focuses on the introduction of Neolithic extraction practices across Europe through to the Atlantic periphery of Britain and Ireland. The key research questions are when and why these practices were adopted, and what role extraction sites played in Neolithic society. Neolithic mines and quarries have frequently been seen as fulfilling economic roles linked to the expansion of the Neolithic economy. However, this ignores the fact that many communities chose to selectively dig for certain types of stone in preference to others, and why the products from these sites were generally deposited in special places such as wetlands. To address this question, 168 near-global ethnographic studies were analysed to identify common trends in traditional extraction practises to produce robust statistics about their motivations and material signatures. Repeated associations emerged between storied locations, the organisation of extraction practises, long-distance distribution of products, and the material evidence such activities left behind. Finally, the new ethnoarchaeological model has been used to analyse the social context of 79 Neolithic flint mine and 51 axe quarry excavations in Britain and Ireland, and to review their European origins. The evidence which emerges confirms the pivotal role played by Neolithic extraction practices in European Neolithisation, and that the interaction of indigenous foragers with migrant miner/farmers in Britain, Ireland and elsewhere was fundamental to the adoption of the new agro-pastoral lifestyle.

Neolithic period. --- Europe --- Great Britain

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