U.S.-Brazil Cooperative Research: Partial Differential Equations & Several Complex Variables

该奖项支持合作研究的部分不同- 弗朗索瓦博士和他的同事们 罗格斯大学的Treves博士和P.D.科达罗 巴西圣保罗，圣保罗大学。 这项工作将 在不同的情况下研究局部解的存在性- 基本复合物起源于 复向量场（光滑真实的流形上）。 最近 Cordaro和Treves得到了一般必要条件， 至少当特征集的秩为时。1. Cordaro Treves目前正在调查 充分条件的证明，特别是在 柯西-黎曼结构的重要例子。 有一个 自然猜想，等待证明，在顶级的情况下， 形式：局部可解性应该保持，如果Levi形式是 在任何一点上都不确定（积极或消极）。 这类结果是完成 亚解析结构理论， 在过去的十年里，通过特里夫斯和他的努力， 合作者 该奖项将允许科达罗特里维斯得到 定期聚在一起做这个项目。 Cordaro从CNPq NSF的相应机构获得资金， 巴西访问罗格斯大学。 特里夫斯和一个毕业生 学生们将访问圣保罗作为回报。

This award supports cooperative research on partial differ- ential equations and complex variables between Dr. Francois Treves of Rutgers University and Dr. P. D. Cordaro of the University of Sao Paulo, Sao Paulo, Brazil. The work will investigate the existence of local solutions in the differ- ential complexes originating from commuting systems of complex vector fields (on a smooth real manifold). Recently Cordaro and Treves have obtained general necessary conditions, at least when the rank of the characteristic set is . 1. Cordaro & Treves are currently investigating the possibility of proving sufficient conditions, in particular in the important case of Cauchy-Riemann structures. There is a natural conjecture that awaits proof, in the case of top-degree forms: local solvability ought to hold if the Levi form is not definite (positive or negative) at any point. This type of result is an essential part of the completion of the theory of hypo-analytic structures that has been building for the last ten years, through the efforts of Treves and his collaborators. The award will allow Cordaro & Treves to get together at regular intervals to work on this project. Cordaro has funds from CNPq NSF's corresponding agency in Brazil to visit Rutgers University. Treves and a graduate student will visit Sao Paulo in return.