Explore the application of zigzag persistence from Topological Data Analysis (TDA) to study the topological evolution of time-evolving graphs and hypergraphs in this 54-minute lecture by Audun Myers. 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 methodology through case studies involving cyber security and social network datasets, gaining insights into how the topological structure of temporal hypergraph representations can reveal underlying dynamics. Enhance your understanding of advanced techniques in graph theory, TDA, and their intersection with real-world complex systems analysis.