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This colloquium talk explores how colored-matching numbers can be integrated into a Lorentzian polynomial framework. Learn about the mathematical connections between tropical geometry of compactifications and convex geometry of degrees of divisors as Chris Eur from Carnegie Mellon University presents research findings as part of the 2025 Program for Women+ and Mathematics at the Institute for Advanced Study. The presentation demonstrates where to find these "log-concave rainbows" through specialized mathematical methods that bridge multiple geometric approaches.