系列讲座: A GENTLE INTRODUCTION TO GROUP STABILITY
报告人: 江永乐（大连理工大学）
时间：
讲座一：2023年7月23日， 北京时间14：00-16：00
讲座二：2023年7月24日， 北京时间10：00-12：00
讲座三：2023年7月25日， 北京时间10：00-12：00
地点：维格堂319
摘要：Roughly speaking, a countable discrete group G is stable with respect to a given norm if each of its approximate representations is close to a genuine representation. The study of group stability has its root in some operator theory problems asked by Halmos and Rosenthal independently. Nowadays, this topic has been studied extensively by people with different background, e.g. dynamical systems, group theory and operator algebras etc. In these three lectures, we plan to give a gentle introduction to this topic.
In lecture 1, we introduce some background on studying group stability, and sketch the proof of Hadwin-Shulman's criterion on characterizing amenable Hilbert-Schmidt stable groups.
In lecture 2, we introduce the recent advance made by Levit-Vigdorovich (arXiv: 2206.02268) and Eckhardt-Shulman (arXiv: 2207.01089) independently on finding new amenable Hilbert-Schmidt stable groups. We sketch the proof due to Levit-Vigdorovich on when metabelian groups are Hilbert-Schmidt stable.
In lecture 3, we discuss the state-of-art on studying other related stability problems for groups and some open problems related to these.
报告人简介：大连理工大学威尼斯人 副教授，主要从事算子代数和遍历论相关的研究工作。在Math. Ann.，J. Funct. Anal.，Ergodic Theory Dynam. Systems，J. Operator Theory等国际学术期刊发表多篇科研论文。