Explore the application of topological data analysis to spatial complex systems in this one-hour lecture by Mason Porter. Delve into the use of persistent homology for analyzing various spatial systems, from leaf venation patterns to the spread of COVID-19. Learn about filtered simplicial complexes that incorporate spatial information and examine diverse examples, including voting patterns in presidential elections, city street networks, and spider webs created under the influence of different drugs. Gain insights into the global structure of spatial systems, distance-based instructions, and new constructions for analyzing spatial data. Understand the key concepts of front propagation, adjacency, and filtration in topological data analysis. Compare different approaches and develop intuition for applying these techniques to real-world data sets. Conclude with a discussion on social contact networks and participate in a Q&A session to deepen your understanding of this fascinating field.