报告题目：Topological K-theory of discrete groups
报 告 人：Bailing Wang
所在单位：The Australian National University
报告时间：2023年5月19日 10:30-11:30
报告地点：腾讯会议：516-539-518
报告摘要: In the 1980’s motivate by the Atiyah-Singer index formula, Baum and Connes constructed a topological K-theory of a discrete group $\Gamma$, together with an assembly map $\mu$ from this mysterious group to the K-theory group of the reduced C^∗ -algebra of $\Gamma$. They conjectured that this assembly map is an isomorphism. The validity of this conjecture implies Novikov conjecture, Gromov-Lawson-Rosenberg conjecture and Kadison-Kaplansky conjecture.
The mathematical details of this construction and the well-definedness of the assembly map were somewhat missing in their original paper. I will briefly explain some of my earlier work with Paulo Carrillo Rouse on filling up these details, and some recent work with Paulo Carrillo Rouse and Hang Wang on an assembly map to periodic cyclic homology and the Chern-Connes pairing formula for any discrete group.
报告人简介：王百灵，澳大利亚国立大学教授。1998 年 4月毕业于澳大利亚阿德莱德大学并获得博士学位。毕业先后在德国波恩马普所，法国高等科学研究所， 苏黎士大学做博士后和访问学者。2005年至今在澳大利亚国立大学工作。主要研究规范场理论在低维拓扑中的拓扑不变量、twisted K－同调和twisted指标理论、Gromov－Witten模空间和哈密尔顿Gromov－Witten模空间的K-理论等领域。
