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

9981251Nistor这项为期三年的美法数学科学合作奖的获得者是宾夕法尼亚州立大学的Victor Nistor和里昂大学的Thierry Fack和Moulan Benameur。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）联合资助，主要研究与叶形相关的代数。研究者将在他们的研究中使用同调方法（k理论、Hochschild和循环同调）。他们感兴趣的是得到指数定理和研究沿叶的叶作用算子的谱不变量。他们对叶的指数定理的研究将涉及到沿叶的算子的伪微分扩展的双变chen - connes性质。该奖项代表了美国方面向美国国家科学基金会和法国国家科学研究中心（CNRS）提交的联合提案。NSF将承担美国研究者的旅费和生活费，CNRS将支持法国数学家访问美国。该项目利用了互补的专业知识，特别是法国团队在拟议方法方面的专业知识。它将促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.