Noncommutative Geometry Seminar

Date: June 10, 2020

Time: 1:00PM - 2:00PM

Location: Zoom 942810031

Speaker: Jianchao Wu, Texas A&M University

Title: The Novikov conjecture and C*-algebras of infinite dimensional nonpositively curved spaces

Abstract: The rational strong Novikov conjecture is a prominent problem in noncommutative geometry. It implies deep conjectures in topology and differential geometry such as the (classical) Novikov conjecture on higher signatures and the Gromov-Lawson conjecture on positive scalar curvature. Using C*-algebraic and K-theoretic tools, we prove that this conjecture holds for any discrete group admitting an isometric and proper action on a (possibly infinite-dimensional) nonpositively curved space that we call an admissible Hilbert-Hadamard space, partially extending earlier results of Kasparov and Higson-Kasparov. In particular, our result can be applied to geometrically discrete subgroups of the group of volume preserving diffeomorphisms of a closed smooth manifold, as they act on an infinite-dimensional symmetric space called the space of L^2-Riemannian metrics. A crucial ingredient of our proof is the construction of C*-algebras from infinite dimensional nonpositively curved spaces. This is joint work with Sherry Gong and Guoliang Yu.

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