Noncommutative Geometry Seminar

Date: October 16, 2019

Time: 2:00PM - 2:50PM

Location: BLOC 628

Speaker: Jianchao Wu, Texas A&M University

Title: The K-theory of C*-algebras associated to certain infinite dimensional spaces

Abstract: Noncommutative geometry provides a potent approach to the study of the algebraic geometry (e.g., K-theory) of infinite dimensional manifolds. In this talk, I will outline the construction of C*-algebras associated to Hilbert-Hadamard spaces, understood as a kind of (typically infinite dimensional) nonpositively curved manifolds. Under mild assumptions, these C*-algebras retain a remnant of Bott periodicity, which we exploit to prove the Novikov conjecture of geometrically discrete groups of diffeomorphisms. This is joint work with Sherry Gong and Guoliang Yu.