In topological data analysis (TDA), one often studies the shape of data by constructing a filtered topological space, whose structure is then examined using persistent homology. However, a single filtered space often does not adequately capture the structure of interest in the data, and one is led to consider multiparameter persistence, which associates to the data a space equipped with a multiparameter filtration. Multiparameter persistence has become one of the most active areas of research within TDA, with exciting progress on several fronts. In this article, we introduce multiparameter persistence and survey some of this recent progress, with a focus on ideas likely to lead to practical applications in the near future.

翻译：在拓扑数据分析（TDA）中，研究者通常通过构建过滤拓扑空间来研究数据的形状，并借助持续同调分析其结构。然而，单个过滤空间往往不足以充分捕捉数据中感兴趣的结构特征，因此需要引入多参数持续性，即为数据配备一个具有多参数过滤的空间。多参数持续性已成为TDA领域最活跃的研究方向之一，在多个前沿上取得了令人瞩目的进展。本文介绍多参数持续性并综述这些近期进展，重点关注那些有望在近期实现实际应用的思路。