Monday, November 16 2015
11:30 - 12:30

#### The Atiyah-Singer index theorem describes a deep relation between theanalytic and geometric-topological properties of a compact smooth manifold.Further development of the theory by Atiyah, Patodi and Singer establishedthe existence of certain spectral invariants which are again intricatelyrelated with the underlying geometry and topology. The Baum-Connesconjecture is a far reaching generalization of the index theorem, and deepresults due to Keswani and Piazza-Schick assert that the spectralinvariants defined by Atiyah-Patodi-Singer have various stabilityproperties when the Baum-Connes conjecture holds. Similar stability resultshold for $\ell^2$ rho-invariants, a generalization of classicalrho-invariants that was first introduced by Cheeger and Gromov. Building onearlier work by Higson and Roe on the analytic surgery exact sequence, wegive a more conceptual framework for the relation of $\ell^2$-rhoinvariants with the Baum-Connes conjecture and give new proofs of the aboveclassical results, introducing new analytic and geometric invariants in theprocess. (joint work with M.-T. Benameur)

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