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Explore the semialgebraic set of linear subspaces with fixed dimension that intersect a given polytope in this 51-minute mathematical lecture. Discover how this set can be described as a union of cells in the complement of a Schubert arrangement associated with the polytope within the Grassmannian. Focus specifically on subspaces that intersect simplicial polytopes and examine their connections to other well-studied semialgebraic subsets of the Grassmannian, including the totally non-negative Grassmannian and the amplituhedron. Learn about cutting-edge research in algebraic geometry and its applications to amplitude theory through work conducted jointly with Sebastian Seemann, presented as part of the Erwin Schrödinger International Institute's thematic programme on Amplitudes and Algebraic Geometry.
