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Explore the convergence of applied topology and discrete structures in this comprehensive lecture. Delve into the rich history of discrete structures in applied mathematics, including graphs and hypergraphs used to model social networks, biological systems, and academic collaborations. Discover how network science and hypernetwork science have been effectively applied to analyze these discrete structures. Learn about recent developments in applied topology, such as persistent homology, mapper, and sheaves, and their successful applications. Examine the speaker's research focusing on the intersection of these two fields, applying topological concepts to study discrete structures that model real data. Gain insights into theoretical topics, including an introduction to hypernetwork science and its relationship to traditional network science, topological interpretations of graphs and hypergraphs, and the dynamics of topology and network structures. Explore practical applications of these concepts through real-world data set examples presented throughout the talk.
