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Explore Borsuk-Ulam theorems extended to higher-dimensional codomains in this 50-minute lecture by Henry Adams. Delve into generalizations of the classical theorem, examining odd maps from n-dimensional spheres into higher-dimensional Euclidean spaces. Learn about small-diameter subsets of spheres whose images contain the origin in their convex hull, with a focus on sharp diameter bounds for odd maps from circles into R^{2k+1}. Investigate open questions regarding optimal diameters for n-spheres mapped into R^{n+1} and R^{n+2}, and discover connections to Schur polynomials. Access accompanying slides and the corresponding paper for further study. This talk, presented for the Rocky Mountain Algebraic Combinatorics Seminar, covers topics including the Classical Coulomb Theorem, historical context, theorem variations, proofs, and algebraic aspects.
