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Explore a 43-minute conference talk from the Amplituhedra, Cluster Algebras, and Positive Geometry Conference where UC Berkeley's Yelena Mandelshtam delves into the combinatorics and geometry of Grasstopes in the m=1 case. Learn how Grasstopes, which are linear projections of the totally nonnegative Grassmannian to a smaller Grassmannian, serve as generalizations of the amplituhedron - a crucial geometric object in physics scattering amplitude calculations. Discover how m=1 Grasstopes can be characterized through unions of cells in hyperplane arrangements with specific sign variation conditions, and understand why amplituhedra are considered minimal Grasstopes. The presentation covers collaborative research conducted with Dmitrii Pavlov and Lizzie Pratt, offering insights into these mathematical structures that bridge geometry and theoretical physics.
