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This volume contains extended abstracts outlining selected talks
and other selected presentations given by participants of the
workshop "Positivity and Valuations", held at the Centre de Recerca
Matematica (CRM) in Barcelona from February 22nd to 26th, 2016.
They include brief research articles reporting new results,
descriptions of preliminary work or open problems, and the outcome
of work in groups initiated during the workshop. The general
subject is the application of valuation theory to positivity
questions in algebraic geometry. The topics covered range from
purely algebraic problems like finite generation of semigroups and
algebras defined by valuations, and properties of the associated
Poincare series, to more geometric questions like resolution of
singularities and properties of Newton-Okounkov bodies, linked with
non-archimedean geometry and tropical geometry. The book is
intended for established researchers, as well as for PhD and
postdoctoral students who want to learn more about the latest
advances in these highly active areas of research.
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