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{\Large Department of Mathematics, BGU}

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{\Huge Colloquium}\\[0.2\baselineskip]

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\textbf{On} \emph{Tuesday, June 16, 2015}
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\textbf{At} \emph{14:30 -- 15:30}
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\textbf{In} \emph{Math -101}

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{\large\scshape Antoine Ducros 
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  (Paris 6)
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will talk about
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{\Large\bfseries Geometry over p-adic fields: Berkovich's approach\par}
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\textsc{Abstract:}
p-adic fields have been introduced by number theorists for arithmetic purposes. Such a field is complete with respect to an absolute value with some strange behaviour: for example, every closed ball with positive radius is open, and every point of such a ball is a center. Because of those properties, to develop a relevant geometric theory over p-adic fields is non-trivial: one can not naively mimic what is done in real or complex geometry, and one has to use a more subtle approach.
In this talk we will present that of Berkovich. His main idea consists in ``adding a lot of points to naive p-adic spaces'' in order to get good topological properties, like local compactness or local path-connectedness. After having given the basic definitions, we will investigate some significant examples, and give a survey of some of the (numerous) applications of the theory has had in various areas (spectral theory, dynamics, algebraic and arithmetic geometry…).








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