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

9981251 Nistor这项为期三年的美法合作数学科学奖由宾夕法尼亚州立大学的Victor Nistor和里昂大学的Thierry Fack和Moulan Benameur获得。该项目在国家科学基金会和法国国家科学研究中心(CNRS)的联合计划下支持，是一项与叶层相关的代数研究。研究人员将在他们的研究中使用同调方法(K-理论、Hochschild和循环同调)。他们感兴趣的是获得指数定理和研究沿叶层作用的算子的谱不变量。他们对叶的指数定理的方法将涉及沿叶的算子的伪微分扩张的双变量Chern-Connes性质。该奖项代表了美国方面向NSF和法国国家科学研究中心(CNRS)提出的联合建议。NSF将支付美国调查人员的旅费和生活费，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中的专门知识。它将增进对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.