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Explore a 51-minute conference talk from the Amplituhedra, Cluster Algebras, and Positive Geometry Conference where MIT & UC Davis researcher Melissa Sherman-Bennett delves into the fascinating connection between cluster algebras and amplituhedron tilings. Discover how physicists Arkani-Hamed and Trnka introduced the amplituhedron concept to enhance understanding of scattering amplitudes in N=4 super Yang-Mills theory. Learn about the amplituhedron's definition as an image of the totally nonnegative Grassmannian, examining key examples including cyclic polytopes, the totally nonnegative Grassmannian itself, and cyclic hyperplane arrangements. Gain insights into collaborative research with Even-Zohar, Lakrec, Parisi, Tessler and Williams focusing on BCFW tilings of m=4 amplituhedra and their unexpected relationship to the Grassmannian's cluster algebra structure.
