U.S.-Brazil Cooperative Research in Differential Geometry

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This project will support a group of U.S. mathematicians under the leadership of Professor H. Blaine Lawson, Jr., of SUNY at Stony Brook, to collaborate with a group of Brazilian mathematicians headed by Professor M. do Carmo of the Institute for Pure and Applied Mathematics (IMPA), located in Rio de Janeiro, Brazil. In general, these mathematicians intend to continue a very successful research exchange that has grown over the past twenty years mainly in the fields of Differential Geometry and Dynamical Systems. Funding will go to support travel by six distinguished U.S. mathematicians to Brazil over the span of two years, to work interactively on the following topics: minimal submanifolds, isometric conversions, conformal geometry, Yang-Mills theory, Backlund transformations, and other related topics. The past two decades have witnessed the growth of the Brazilian School of Differential Geometry to become one of major stature. Some of the best results of this school have been in the area of submanifold theory; in several cases these results have led to collaborative work with U.S. mathematicians where both sides have benefited. One need only mention, among others, the fundamental pioneering work of Barbosa and do Carmo on the structure of stable surfaces, and the complete classification of compact conformally flat hypersurfaces in euclidean space achieved by members of the Brazilian school (Dajczer, do Carmo, Mercuri). This project will bring together a group of productive U.S. mathematicians who either already have established collaborations with Brazilian mathematicians or whose work is likely to inspire new activity to continue the direct exchange of ideas that is of vital importance for mathematical research.