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This lecture explores the fascinating phenomenon of self-organized vegetation patterns in drylands, focusing on how water-limited ecosystems develop regularly-spaced bands of vegetation that form perpendicular to gentle slopes to capture rain runoff. Discover how these large-scale patterns, visible in satellite imagery across semi-arid and arid regions worldwide, emerge through consumer-resource interactions between biomass and soil moisture. Learn about the PDE framework used to model these interactions, with particular attention to how rainstorms—modeled as impulses to the system—affect pattern formation. Examine research investigating the impact of storm variability on these patterns by introducing randomness into storm timing and water volume, providing potential insights into dryland ecosystem resilience in the face of climate change. The presentation, delivered by Mary Silber on April 3, 2025, offers valuable understanding of these complex ecological systems through mathematical modeling approaches.