报告时间：2025年5月11日 10:00开始
报 告 人：张国华（复旦大学）
报告地点：9-113
报告题目：Comparison Property for Groups of Subexponential Growth
报告摘要:The comparison property of countable amenable groups originates in the theory of C∗-algebras, and is closely related to the property of almost finiteness introduced recently by H. Matui for ample groupoids and appliedsubsequently by others to problems in classification of C∗-algebras. But the most important thing for us is the “dynamical” version of the comparison property which concerns group actions on compact metric spaces. In this setup it was defined by J. Cuntz and further investigated by M. Rørdam and W. Winter.Let a countable discrete group G act on a zero-dimensional compact metric space X. We say that the action admits comparison if for any clopen sets A and B, the condition, that for every G-invariant measure m on X we have the sharp inequality m(A)< m(B), implies that there exists a finite clopen partition A1, ..., Ak for A, and elements g1, ..., gk in G such that g1(A1), ..., gk(Ak) are disjoint clopen subsets of B. We prove this property for actions by groups of subexponential growth.This is a joint work with Professor Tomasz Downarowicz.
报告人简介：张国华，复旦大学数学科学学院教授，博导。主要研究动力系统的复杂性理论和可数离散群作用系统的熵理论。在Memoirs Amer. Math. Soc., J. Reine Angew. Math., Adv. Math, ETDS, J. Mod. Dyn., JFA, JDE等国际知名期刊上发表多篇论文。承担国家自然科学基金优秀青年基金，国家自然科学基金面上项目等多项科研项目。
