报告时间：2025年11月28日（周五）上午 11:00-11:50

报告地点：苏州大学天赐庄校区精正楼306

报告人：邓金涛，上海财经大学

Abstract：

The coarse Baum-Connes conjecture provides an algorithm to compute the higher index of elliptic operators on Riemannian manifolds. It has been verified for a large class of metric spaces. To study this conjecture for a larger class of metric spaces, we introduce a twisted coarse Baum–Connes conjecture with stable coarse algebras, which can be viewed as a geometric analogue of the Baum–Connes conjecture with coefficients.This twisted version has stronger permanence properties than the classical coarse Baum–Connes conjecture, particularly with respect to subspaces.

This framework can be used to study the relatively hyperbolic groups. For a finitely generated group G that is hyperbolic relative to {H_1,...,H_n}, the group G satisfies twisted coarse Baum-Connes conjecture with stable coefficients, if and only if each H_i does. This is a joint work with Ryo Toyota.

报告摘要：

粗Baum-Connes猜想为计算黎曼流形上椭圆算子的高指标提供了一种算法。该猜想已在很大一类度量空间上得到验证。为了将这一猜想推广至更大类度量空间，我们引入了带有稳定粗代数的扭曲粗Baum–Connes猜想，这可以看作是带系数的Baum–Connes猜想的几何类比。该扭曲版本相较于经典的粗Baum–Connes猜想具有更强的持久性，特别是在子空间的情形下。

该框架可用于研究相对双曲群。对于一个有限生成群 G，它相对于群 {H1,…,Hn}是双曲的，则 G满足带有稳定系数的扭曲粗Baum–Connes猜想，当且仅当每一个 Hi都满足该猜想。本工作是与Ryo Toyota合作完成的。

邀请人：梁兵兵