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

University Of Illinois At Chicago, Chicago IL

Investigators

Abstract

NSF-CNPq Collaborative Research Proposal on solitons, integrable theories and inifite-dimensional symmetries: This is a proposal for a travel grant within the NSF-CNPq Collaborative Research program. 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. Gomes and A.H. Zimerman (State University of Sao Paulo) on fundamental features of integrability and further development of its applications in a variety of modern physical contexts. The collaborators plan to combine efforts to improve knowledge of various integrable models in two and higher dimensions, their algebraic and analytic aspects and ties between them. They expect to make advances on the following topics: understanding of new integrable models (with and without supersymmetry) emerging from deformations of bihamiltonian structures; construction of non-abelian Toda models with internal degrees of freedom and its soliton solutions; the Riemann-Hilbert factorization problem applied to gradations other than the homogeneous ones and the tau functions of topological field theories described by the Witten-Dijkgraff-Verlinde-Verlinde equation; and soliton solutions of higher-dimensional integrable models and their structure. The broader impacts resulting from the proposed activity are in the educational component. Its objectives are to train young researchers in new methods and techniques of the theory of integrable systems and their applications. There are a large number of graduate students in the Brazilian hosts institutions of Drs. Ferreira, Gomes and Zimerman The travel grant will involve all senior collaborators in training and mentoring arrangements. Several former Brazilian students and one US student now hold academic positions and continue to contribute to the field.