Noncommutative Geometry Seminar

Date: January 16, 2019

Time: 2:00PM - 3:00PM

Location: BLOC 628

Speaker: Jianchao Wu, Pennsylvania State University

Title: The Novikov conjecture, the group of volume preserving diffeomorphisms, and Hilbert-Hadamard spaces

Abstract: The Novikov conjecture is a central problem in manifold topology. Noncommutative geometry provides a potent approach to tackle this conjecture. Using C*-algebraic and K-theoretic tools, we prove that the Novikov conjecture holds for any discrete group admitting an isometric and metrically proper action on an admissible Hilbert-Hadamard space, which is an infinite-dimensional analogue of complete simply connected nonpositively curved Riemannian manifolds. In particular, these groups include geometrically discrete subgroups of the group of volume preserving diffeomorphisms of a compact smooth manifold with a fixed volume form. This is joint work with Sherry Gong and Guoliang Yu.