Report title: Band truncation approximations for operators in lp uniform Roe algebras and applications

Reporter: Professor Wang Qin East China Normal University

Reporting time: 14:30-15:30, December 4, 2020

Report location: Tencent Conference ID: 253 251 669 Password: 123456

School contact: Zhang Yuanhang zhangyuanhang@jlu.edu.cn

Report summary:

Uniform Roe algebras are typically C*-algebras on discrete metric spaces which reflect large scale geometry of the underlying spaces. Recently, the l^p versions of uniform Roe algebras have attracted muchattention due to their applications in operator theory, operator algebras and K-theory.

In this talk, we will determine a large class of dense subspaces of l^p uniform Roe algebras of discrete groups whose elements can be approximated in operator norm by their band truncations. Under an l^p version of Rapid Decay condition, we construct a spectral invariant subalgebra of the l^p uniform Roe algebra of a discrete group. We also establish that the K-theory groups of these l^p operator algebras on discrete metric spaces with Yu's property (A) depend continuously on p.

Brief introduction of the speaker:

Wang Qin is a professor and doctoral tutor at the Center for Operator Algebra, School of Mathematical Sciences, East China Normal University. He is mainly engaged in the research of operator algebra, rough geometry, non-commutative geometry and other fields. He is involved in the important problem of non-commutative geometry "rough Baum-Connes conjecture" "Cross Novikov Conjecture" and other aspects have made some important results, won the National Hundred Excellent Doctoral Dissertation Award, selected into the New Century Excellent Talents Support Program of the Ministry of Education, Shanghai Shuguang Scholar, Shanghai Pujiang Scholar, in J. Reine Angew . Math., Adv. Math., J. Funct. Anal. and other international authoritative journals published more than 30 papers.