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Physical mathematics of integrable systems


This research proposal intends to investigate several aspects related to the Physical Mathematics of two-dimensional integrable models. We will consider the exact solution of vertex models of Statistical Mechanics based on the Uq[SU(2)] quantum group at roots of unity, on the classical exceptional Lie algebras and superalgebras, on the non-compact SL(2,R) algebra as well as extensions of the Hubbard Model. In these systems we shall study both their mathematical properties of integrability and their potential applications to Field Theory and Condensed Matter. We hope to apply and to develop tools that will help us to unveil the physical behaviour of integrable systems such as the nature of their elementary excitations, thermodynamics and correlation unctions of observables. (AU)

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