The representation theory of rational Cherednik algebras.

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The aim of this project is to advance our understanding of the representation theory of rational Cherednik algebras at t=0. These algebras have a very rich representation theory which is still poorly understood. Moreover, they have close links to integrable systems, combinatorics and algebraic geometry - a better understanding of the representation will have applications in all these areas. In this project we propose to use the theory of symmetric algebras to completely classify when the (restricted) rational Cherednik algebra has finite, tame or wild representation type. In thecases where the representation type is finite or tame, we will completely classify all indecomposable modules for these algebras.