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Explore a 47-minute lecture from Harvard CMSA's Workshop on Nonlinear Algebra and Combinatorics from Physics where Matteo Parisi delves into the fascinating world of Amplituhedra and their connections to particle physics. Learn about these Grassmannian generalizations of polytopes and their crucial role in encoding elementary particle interactions in Quantum Field Theories. Discover how triangulations of Amplituhedra relate to computing scattering amplitudes in N=4 super Yang-Mills theory, building upon foundational concepts like Stasheff's associahedron and Gelfand's secondary polytopes. Examine the interplay between triangulation combinatorics and String Theory's T-duality, particularly in relation to the Momentum Amplituhedron. Investigate a newly discovered duality between m=2 type Amplituhedra and the Hypersimplex - a significant polytope in matroid theory and tropical geometry. Follow along as the presentation progresses from basic geometric concepts through advanced applications, concluding with insights from collaborative research with Lauren Williams, Melissa Sherman-Bennett, and Tomasz Lukowski.
