Explore the application of zigzag persistence from Topological Data Analysis (TDA) to study the topological evolution of time-evolving graphs and hypergraphs in this one-hour conference talk. Delve into the power of temporal hypergraphs for modeling complex systems with multi-way interactions and temporal dynamics. Learn how this innovative approach addresses the limitations of existing tools in capturing the evolving topological structure of temporal hypergraphs over time. Examine the practical applications of this pipeline through case studies in cyber security and social network datasets, gaining insights into how the topological structure of temporal hypergraph representations can reveal underlying dynamics. Discover a new perspective on data analysis that combines advanced mathematical concepts with real-world applications, enhancing your understanding of complex system evolution.