Mathematical Sciences: Symplectic Geometry and Euclidean Geometry

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9504134 Millson The proposed research lies in the interface of topology and geometry. Working on the classical problem of classifying linkages in space, the investigator has found connections to representation theory and algebraic geometry. To be more specific, the proposed research seeks to develop parallels between the singularities in the representation varieties of Coxeter groups and the singularities in the deformation spaces of linkages. A linkage in space can model a robot arm and other rigid structures with joints; a topological classification of possible linkages in space may turn out to have ramifications in control theory and robotics.