This award supports cooperative research in applied mathematics to be conducted by Tadeusz Balaban of Boston University and Ricardo Schor and Michael O'Carroll of the physics department of the Federal University of Minas Gerais in Belo Horizonte, Brazil. The problem is the ultraviolet stability of three- dimensional spinor quantum electrodynamics and the application of renormalization group methods to low temperature classical spin models, such as the Heisenberg model. These researchers have been working on infrared properties of small perturbation models of the free lattice electromagnetic field and a renormalization group approach to spinor electrodynamics. In the first case they have proved the infrared asymptotic freedom for these models and have recently published the results. For the second problem, the two-dimensional model of spinor electrodynamics is well known but the three- dimensional model is a much more difficult problem. They have started work on the latter case using the renormalization group approach. This award will support this new work in which the ultraviolet stability will be investigated, first for two-dimensional classical spin models and then, after modifications, for the three-dimensional case thus extending a successful and productive preliminary collaboration.
