Mathematical Sciences: String Equations in Mathematical Physics and Integrable Systems

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This research concerns string equations in mathematical physics and integrable systems. In particular, the research concerns the solutions of partial differential equations related to quantum field theory and string theory that may have solutions representable as special types of Feynman type integrals. The project will also concern isopectral manifolds of differential operators and boundaries. In particular, what is the behavior of the differential operators and how does one regularize the differential operators near their blow-up locus. This research is in the general area of geometric analysis and mathematical physics and illustrates the exciting interaction between mathematics and physics, especially in quantum field theory and string theory where there is a circle of ideas involving integrable systems, module space, algebras, and matrix models.