Ëã×Ó´úÊýÖÐÐÄ¶Ì¿Î³Ì£º$K$-theory and $L^p$ uniform Roe algebras

YeongChyuan Chung  (IMPAN)

10:00-12:00, 14:00-16:00, Oct 30-31, 2018   Science Building A510

Abstract:

Quantitative $K$-theory for $C^\ast$-algebras originated in the work of Guoliang Yu on the Novikov conjecture and the coarse Baum-Connes conjecture. More recently, it has also been used to study the $K$-theory of various classes of $C^\ast$-algebras and has been generalized to be applicable to more general Banach algebras. In this series of lectures, I will give an introduction to the notion of quantitative $K$-theory for Banach algebras. I will also present some joint work with Kang Li on $L^p$ uniform Roe algebras associated to metric spaces with bounded geometry. One result is about surjectivity of the map on K_0 groups induced by the diagonal inclusion when the metric space has asymptotic dimension one, and this will be an example where quantitative $K$-theory is used. Another result (not involving $K$-theory) is about the rigidity of these algebras, which indicates that they are (possibly) more rigid when p is not 2 than when p=2.