U.S.-Brazil Cooperative Research in Differential Geometry

该项目将支持一组美国数学家， H教授的领导。小布莱恩·劳森关于SUNY at Stony 布鲁克，与一群巴西数学家合作， 由M教授领导。纯粹和科学研究所的杜卡莫 应用数学（IMPA），位于巴西里约热内卢。 在 一般来说，这些数学家打算继续一个非常成功的 在过去的二十年里，研究交流主要是 在微分几何和动力系统领域。 资金将用于支持六位美国杰出人士的旅行。 数学家们在两年的时间里来到巴西， 交互式地讨论以下主题：极小子流形， 等距变换，保形几何，杨-米尔斯理论， 贝克兰德变换，以及其他相关主题。 过去二十年见证了巴西人的成长 成为微分几何学院的一个重要地位。 这所学校的一些最好的结果已经在该地区 子流形理论;在一些情况下，这些结果导致 与美国数学家合作，双方都有 受益。 我们只需要提到，除其他外， 巴博萨和卡尔莫关于稳定结构的开创性工作 曲面，以及紧致共形曲面的完整分类 欧氏空间中的平坦超曲面， 巴西学校（Dajczer，do Carmo，Mercuri）。 该项目将 汇集了一群富有成效的美国数学家， 要么已经与巴西建立了合作关系， 数学家或其工作可能激发新的活动， 继续直接交换意见，这至关重要 用于数学研究。

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.