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Explore the fascinating intersection of topology, graph theory, and artistic sculpture in this mathematical lecture that delves into the practical construction of maximal complete maps on surfaces. Learn about the "other map coloring theorem" established by Gerhard Ringel and John William Theodore Youngs in the late 1960s, which determines the chromatic number of closed orientable surfaces based on their genus, predating the famous four color theorem. Discover the challenge of moving beyond theoretical results to actual map construction, specifically focusing on creating maps with exactly X regions where every pair of regions shares a boundary line. Follow the speaker's mathematical journey to design such complete maps on the Rulpidon, a genus-3 surface created by French sculptor Ulysse Lacoste, demonstrating how mathematical research can be enhanced through artistic collaboration and visual illustration techniques.
