Speaker: Kang Li (Friedrich-Alexander-Universität Erlangen-Nürnberg)
Time: 2025-Sep-05th 14:30:00
Location: R1410, SIMIS
Abstract:
This lecture opens a three-part series on the structure of ideals in reduced groupoid $C^*$-algebras, with a particular emphasis on their supports and dynamical properties. The series explores foundational results, the concepts of inner and outer supports, and recent advances — including joint work with Jiawen Zhang — on ghostly ideals and their applications to regular ideals, tracial ideals, and the amenability problem for Thompson’s group~$F$.
In this first lecture, I will introduce the basic properties of \’etale groupoids and present key classes of examples, such as transformation groupoids and coarse groupoids. I will then outline the proof of a theorem, obtained in joint work with Christian B\”onicke (2018), which shows that all ideals in a reduced groupoid $C^$-algebra~$C_r^(G)$ are dynamical if and only if the underlying \’etale groupoid~$G$ is inner exact and has the residual intersection property. An ideal~$I$ is called dynamical if it is uniquely determined by an open invariant subset $U \subset G^0$, equivalently if it is generated by~$C_0(U)$ inside~$C_r^*(G)$.
Speaker introduction:
Kang Li is a Danish mathematician specializing in operator algebras and their applications to dynamical systems, geometric group theory, and representation theory. He has published over 30 papers in leading journals, including IMRN, Journal of Functional Analysis, Advances in Mathematics, and Ergodic Theory and Dynamical Systems. His research interests closely align with those of Fudan University and East China Normal University, with which he has maintained extensive collaborations.
English 
简体中文