Mathematical Sciences: Geometric Applications of Exterior Differential Systems

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The research entails questions concerning the properties of subvarieties of projective space using the geometry of exterior differential systems and partial differential equations. These methods may be instrumental in obtaining progress on some important questions and conjectures in algebraic geometry. The research also entails developing certain geometric features of certain algorithmic systems. The overall approach to these questions are likely to have extensions to other branches of pure and applied mathematics.