报告题目：Quasi-local algebras and asymptotic expanders

报 告 人：章嘉雯（复旦大学）

报告时间：2023年4月10日 10:30-11:30

报告地点：威廉希尔中文网站301室

主办单位：威廉希尔中文网站

报告摘要： 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.

This is a joint project with Ana Khukhro, Kang Li, Piotr Nowak, Jan Spakula and Federico Vigolo.

   报告人简介：章嘉雯毕业于复旦大学，师从陈晓漫教授，之后赴维也纳大学和南安普顿大学从事博士后工作，并于2021年入职复旦大学。研究方向是算子代数、高指标理论、粗几何与几何群论，获得了如下成果：（1）引入一类新的指标代数并计算其K-群；利用图论和动力系统工具，构造出高指标理论中处于核心地位的粗Baum-Connes猜想的几类新反例（2）给出渐近维数的新刻画，由此计算几何群论中几类重要空间的渐近维数，为研究其上指标代数提供新角度（3）给出Roe代数和拟局部代数是否相同的判别法，并将极限算子理论推广至群胚情形。研究成果发表在Adv. Math., Trans. AMS., IMRN, JFA等国际知名期刊上。