Combinatorics and Geometry of the Amplituhedron

Explore the fascinating world of the amplituhedron in this 54-minute lecture by Lauren Williams from Harvard University. Delve into the geometric object introduced by Arkani-Hamed and Trnka for computing scattering amplitudes in N=4 super Yang Mills theory. Discover how the amplituhedron generalizes interesting concepts like cyclic polytopes and the positive Grassmannian, while exploring its connections to tropical geometry, cluster algebras, and combinatorics. Begin with a gentle introduction to the amplituhedron before surveying recent progress on key conjectures, including the Magic Number Conjecture, the BCFW tiling conjecture, and the Cluster Adjacency conjecture. Gain insights into the intersection of combinatorics and geometry in this advanced mathematical exploration presented at the Institut des Hautes Etudes Scientifiques (IHES).