Combinatorics of the Amplituhedron
Explore the fascinating world of the amplituhedron in this 49-minute lecture by Lauren Williams from Harvard University. Gain a gentle introduction to this mathematical concept, which was introduced by Arkani-Hamed and Trnka for computing scattering amplitudes in N=4 super Yang Mills. Discover how the amplituhedron is defined as the image of the positive Grassmannian under a map induced by a totally positive matrix. Delve into its connections with various mathematical areas, including cluster algebras, matroids, and combinatorics. Learn about the relationship between the amplituhedron and important mathematical concepts such as Eulerian numbers and Narayana numbers. This talk, presented at the Institut des Hautes Etudes Scientifiques (IHES), offers an accessible entry point into an intriguing area of mathematical physics.