The metric compactification and its applications in analysis and dynamics

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The metric compactification of a metric space has been an object of study in a variety of fields most notably in geometric group theory and dynamics. In recent years some interesting applications in geometric and functional analysis have been found. However, in most settings in analysis there is only a limited amount of knowledge of the structure of the metric compactifications, as in most settings the metric spaces are not proper. One of the objectives of the project is to gain a deeper understanding of the structure of the metric compactification in a variety of important settings in analysis, such as operator algebras, e.g. B(H), and specific classes of Banach spaces. A second objective of the project is to further develop applications of the metric compactification in the dynamics of fixed point free mappings and Denjoy-Wolff type theorems and in fixed point theory. There are some open problems in this field, which are known to be hard, but of significant interest.