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

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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.