Mathematical Sciences: Cyclic Homology, Higher Indices and Secondary Invariants

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Professor Moscovici will exploit the tools of non-commutative differential geometry and of non-commutative harmonic analysis for the investigation of differential and topological invariants of multiply connected manifolds. The first part of his project concerns invariants of index type and is a continuation of his work on the Novikov conjecture. The second part, which represents a new line of research, deals with the more subtle secondary-type invariants (e.g. analytic torsion and the eta invariant) and aims to place them in the framework of cyclic (co)homology and algebraic K-theory. A manifold is the generalization to higher dimensions of a smooth two dimensional surface. For example, the space-time continuum is a four dimension manifold. Professor Moscovici's research is aimed at understanding these geometric objects by exploiting connections with the theory of linear transformations (infinite matrices) in infinite dimensional spaces.