Noncommutative Geometry Seminar

Date: February 14, 2018

Time: 2:00PM - 2:50PM

Location: BLOC 628

Speaker: Zhizhang Xie, Texas A&M University

Title: K-homology and sheaves

Abstract: For smooth manifolds, typical examples of K-homology classes are given by elliptic differential operators. By definition, they are local or infinitesimal in the sense that their propagations are arbitrarily small. The concept of sheaves (again by definition) shares this fundamental property of being local. One naturally expects some close connections between these two important notions. In particular, making some of these connections precise allows us to prove interesting theorems in geometry and topology, such as Gronthendieck-Riemann-Roch theorem for singular varieties. In this talk, I will try to explain some of these connections by discussing some interesting examples. The talk is based on ongoing joint work with N. Higson.