報告題目：Topological K-theory of discrete groups
報 告 人：Bailing Wang
所在單位：The Australian National University
報告時間：2023年5月19日 10:30-11:30
報告地點：騰訊會議：516-539-518
報告摘要: 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.
報告人簡介：王百靈，澳大利亞國立大學教授。1998 年 4月畢業于澳大利亞阿德萊德大學并獲得博士學位。畢業先後在德國波恩馬普所，法國高等科學研究所， 蘇黎士大學做博士後和訪問學者。2005年至今在澳大利亞國立大學工作。主要研究規範場理論在低維拓撲中的拓撲不變量、twisted K－同調和twisted指标理論、Gromov－Witten模空間和哈密爾頓Gromov－Witten模空間的K-理論等領域。
