Mathematical Sciences: Partial Differential Equations and Moduli of Curves and Bundles

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The principal investigator will study some problems in algebraic geometry related to partial differential equations. Systems of partial differential equations may be formulated as an integrable system. The solutions of the partial differential equation are realized as integrable manifolds of the system. It is this formulation of systems of partial differential equations which makes the application of methods from algebraic geometry possible. Systems of partial differential equations play an important role in models of physical systems. An important example is in the area of control theory in which one would like to guide an object along a desired trajectory. The system of partial differential equations used to model this situation can be formulated as an integrable system. The research supported by this award should be particularly useful in studying this problem.