NSF-CNPq Collaborative Research Proposal on solitons, integrable theories and inifite-dimensional symmetries

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NSF-CNPq Collaborative Research Proposal on solitons, integrable theoriesand inifite-dimensional symmetries:This is a proposal for a travel grant within the NSF-CNPq Collaborative Researchprogram. The project will enable continuation of a long-term collaboration of the PI,Professor Aratyn, with Profs. L.A. Ferreira (University of Sao Paulo), and J.F. Gomesand A.H. Zimerman (State University of Sao Paulo) on fundamental features ofintegrability and further development of its applications in a variety of modern physicalcontexts.The collaborators plan to combine efforts to improve knowledge of various integrablemodels in two and higher dimensions, their algebraic and analytic aspects and tiesbetween them. They expect to make advances on the following topics: understandingof new integrable models (with and without supersymmetry) emerging fromdeformations of bihamiltonian structures; construction of non-abelian Toda models withinternal degrees of freedom and its soliton solutions; the Riemann-Hilbert factorizationproblem applied to gradations other than the homogeneous ones and the tau functionsof topological field theories described by the Witten-Dijkgraff-Verlinde-Verlinde equation;and soliton solutions of higher-dimensional integrable modelsand their structure.The broader impacts resulting from the proposed activity are in the educationalcomponent. Its objectives are to train young researchers in new methods andtechniques of the theory of integrable systems and their applications. There are a largenumber of graduate students in the Brazilian hosts institutions of Drs. Ferreira, Gomesand Zimerman The travel grant will involve all senior collaborators in training andmentoring arrangements. Several former Brazilian students and one US student nowhold academic positions and continue to contribute to the field.