Analysis Seminar: "Cyclic Cohomology and Local Index Theory"

Abstract: Given a topological algebra A over the complex numbers, it's cyclic cohomology can be thought of as a generalization of the notion of homology for A. Given a representation of our algebra to the bounded operators on a Hilbert space H, if we equip H with an unbounded self-adjoint D operator compatible with the representation, we obtain a spectral triple. We will show that one can build interesting cyclic cohomology classes for the algebra A with these spectral triples which contain analytic information about the operator D. We will proceed to discuss how one is to compute the given cocycles in practice and showcase some recent results due to the speaker (joint with A. Haj, Y. Loizides).

Host: Yanli Song