Mathematical Sciences: Symplectic Geometry and Euclidean Geometry

9504134米尔逊提出的研究主要集中在拓扑学和几何学的结合上。在对空间中的连杆进行分类这一经典问题上，这位研究者发现了与表示论和代数几何的联系。更具体地说，该研究试图发展Coxeter群表示簇中的奇点与连杆变形空间中的奇点之间的相似之处。空间中的连杆可以为机器人手臂和其他具有关节的刚性结构建模；对空间中可能的连杆进行拓扑分类可能会在控制理论和机器人学中产生影响。

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.