报告题目：Quasi-local algebras and asymptotic expanders

报 告人：章嘉雯 副研究员

时   间：2021年11月11日 19:00-21:00

会议列表：https://meeting.tencent.com/dm/Rc52q6jgE9sM

会议ID：766 780 926

报告人简介：章嘉雯毕业于复旦大学，之后赴奥地利维也纳大学和英国南安普顿大学从事博士后研究工作，并于今年入职复旦大学数学科学学院。章嘉雯的研究领域主要集中在非交换几何、高指标理论、粗几何与几何群论，其研究成果主要有提出粗均值代数的概念并建立其上几何与代数的统一、给出指标代数的内蕴刻画、提出渐近膨胀的概念并将其运用于分析、图论、动力系统等相关领域，包括构造出高指标理论中核心猜想的全新反例等。目前已在国内外知名学术期刊上发表学术论文11篇，包括1篇Advances in Mathematics、1篇Transactions of the American Mathematical Society、2篇Journal of Functional Analysis等；并受邀在国内外学术会议上作重要邀请发言情况。

报告内容：Roe algebras are C*-algebras associated to metric spaces, which encode their large scale structures. These algebras play a key role in higher index theory, providing a bridge between geometry, topology and analysis. We study a quasi-local perspective on Roe algebras, which leads to a larger index algebra called the quasi-local algebra. Based on the idea of quasi-locality, we introduce a graphic notion called asymptotic expanders which generalise the classic one of expanders. Using a structure theorem, we show that asymptotic expanders cannot be coarsely embedded into any Hilbert space and hence construct new counterexamples to the coarse Baum-Connes conjecture.