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Explore the intricate relationship between geometry, topology, and decision-making in this thought-provoking lecture. Delve into the challenges of making choices when faced with conflicting advice from multiple sources or experts. Examine various approaches to decision-making, particularly in scenarios where simple averaging is not feasible due to the non-convex nature of alternatives. Discover how geometric and topological concepts play a crucial role in addressing these complex decision problems. Investigate general theoretical frameworks, including analogues of Arrow's dictatorship theorem, and learn how they can be applied to specific situations. Gain insights into the emerging field of "applied topology" and its quantitative nature in solving real-world decision-making challenges.
