Geometric Banach Property (T) for Cayley graphs and Limit Space Theory
Liang Guo 郭亮 (SIMIS)
14:00-15:00, December 4, 2025 Science Building A503
Abstract:
In recent work, we introduced a notion of geometric Banach property (T) for metric spaces, which parallels the concept of Banach property (T) for groups. While general metric spaces lack group structure?making the characterization of their geometric Banach property (T) challenging?we can derive more elegant descriptions for sequences of Cayley graphs, as the inherent group structure of each graph provides a coherent translation structure. In this talk, we employ nonstandard analysis to construct limit groups for Cayley graph sequences and prove that the geometric Banach property (T) of a Cayley graph sequence implies the Banach property (T) of its limit groups. Moreover, these properties become equivalent under certain conditions. Using the group structure of Cayley graphs, we also study the "coarse group actions" of Cayley graph sequences and investigate the relationships between Banach coarse fixed point property and geometric Banach property (T). This work is based on joint research with Jin Qian and Qin Wang.
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