Noncommutative Geometry Seminar

Date: March 6, 2019

Time: 2:00PM - 3:00PM

Location: BLOC 628

Speaker: Hao Guo, Texas A&M University

Title: A Lichnerowicz vanishing theorem for the maximal roe algebra

Abstract: Let M be a complete spin Riemannian manifold. Then the Dirac operator on M has an index taking values in the K-theory of the maximal Roe algebra. One of the basic properties one would like to have for this index is that it vanishes when the M has uniformly positive scalar curvature. But as distinct from the setting of the reduced Roe algebra, one cannot directly apply a functional calculus argument on the maximal Roe algebra to show this vanishing. In this talk we outline the steps to a proof of this fact using a uniform version of the maximal Roe algebra. This is joint work with Zhizhang Xie and Guoliang Yu.