报告题目：From Equivariant Coarse Embeddings to the Baum-Connes Conjecture: Quasi K-amenability of Hecke Pairs

报告人：姚秀峰 华东师范大学

报告时间：2026年4月27日 14:00-15:00

报告地点：正新楼报告厅106

校内联系人：钟永权 [email protected]

报告摘要：

The Baum-Connes conjecture plays a central role in operator algebras and noncommutative geometry. For discrete groups, analytic properties such as amenability or the Haagerup property (a-T-menability) typically ensure that the conjecture holds. However, for a Hecke pair $(\Gamma, \Lambda)$, the global group $\Gamma$ often exhibits relative Kazhdan's Property (T), which causes these standard analytic conditions to fail. Furthermore, due to the lack of normal subgroups, even classical K-amenability is often too strong in this setting. In this talk, we introduce the concept of "quasi K-amenability," a property requiring only that the canonical quotient map between the maximal and reduced crossed products induces an isomorphism in K-theory. To overcome the absence of a group structure on the coset space $X = \Gamma/\Lambda$, we study the $\Gamma$-equivariant coarse embeddings of $X$ into a Hilbert space. By applying the coarse Dirac-dual-Dirac method and developing a cutting-and-pasting technique on Roe algebras, we reduce the global Baum-Connes problem to local subgroups commensurable with $\Lambda$. We will prove that if the coset space admits a $\Gamma$-equivariant coarse embedding and the subgroup $\Lambda$ is a-T-menable, then $\Gamma$ is quasi K-amenable. As applications of this framework, we will also discuss how these conditions lead to positive results for the Baum-Connes conjecture with coefficients and the strong Novikov conjecture for Hecke pairs.

报告人简介：

姚秀峰，华东师范大学在读博士，研究方向为非交换几何、粗几何、几何群论。