U.S.-France Cooperative Research: Index Theorems, Residues, Eta Invariants, and Foliations

9981251 Nistor美国-法国在数学科学方面的合作涉及宾夕法尼亚州立大学的维克托尼斯托和里昂大学的蒂埃里·法克和穆兰·贝纳穆尔。 该项目由美国国家科学基金会和法国国家科学研究中心（CNRS）的联合项目支持，是一项与叶理有关的代数研究。 研究人员将在他们的研究中使用同源性方法（K理论，Hochschild和循环同源性）。 他们感兴趣的是获得指数定理和研究谱不变量的运营商采取行动沿着叶的叶理。 他们对叶理指数定理的研究将涉及算子沿叶理叶子沿着的伪微分延拓的双变Chern-Connes特征。该奖项代表了美国方面向NSF和法国国家科学研究中心（CNRS）提出的联合提案。 国家科学基金会将支付美国研究员的旅费和生活费，CNRS将支持法国数学家访问美国。 该项目利用了互补的专门知识，特别是法国小组在拟议办法方面的专门知识。 它将促进指数定理和其他相关主题的理解。

9981251NistorThis three-year award for U.S.-France collaboration in mathematical sciences involves Victor Nistor of Pennsylvania State University and Thierry Fack and Moulan Benameur of the University of Lyon. The project, supported under the joint program of the National Science Foundation and the French National Center for Scientific Research (CNRS), is a study of algebras relevant to foliations. The investigators will use homological methods (K-theory, Hochschild, and cyclic homology) in their study. They are interested in obtaining index theorems and in studying the spectral invariants of operators acting along the leaves of foliations. Their approach to index theorem for foliations will involve the bivariant Chern-Connes character of the pseudodifferential extension of operators along the leaves of foliations.This award represents the U.S. side of a joint proposal to the NSF and the French National Center for Scientific Research (CNRS). NSF will cover travel funds and living expenses of the U.S. investigator and the CNRS will support the visits of the French mathematicians to the United States. The project takes advantage of complementary expertise, in particular, the French team's expertise in the proposed approach. It will advance understanding of index theorems and other related topics.