Mathematical Sciences: Integrable Systems and Moduli Problems in Algebraic Geometry

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Emma Previato will continue her research into integrable systems of differential equations and moduli problems in algebraic geometry. She will be studying some of the soliton equations which arise naturally in physics. In particular she will work with the Kadomtsev-Petviashvili equations. These model various standing wave configurations and demonstrate many symmetries. Previato will be investigating the geometrical aspects of this theory. Since the special qualities possessed by these integrable systems are algebraic in nature, her work will have impact in both differential and algebraic geometry. The major objective of the research is to embed integrable systems in moduli spaces in order to gain information on the latter's function theory and properties as projective varieties. This offers potential applications to the study of moduli spaces for vector bundles on curves as well as the possible discovery of some new and interesting finite dimensional integrable systems.