Mathematical Sciences: Flat Connections and Deformation Problems

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The principal investigator will study isomonodromy deformation problems and their application to solve asymptotic connection formulae and to carry out a related study on the factorization problem associated with Gelfand-Dikii flows. These fundamental properties of integrable systems have been established for the 2 x 2 case, but have not been resolved for the general n x n case. A geometrical-analytical understanding is critical for further development. Integrable systems and inverse scattering problems play a fundamental role in establishing links between fundamental physics and the way in which mathematical models are used to describe it.