Melissa Sherman-Bennett | Cluster algebras and tilings of amplituhedra 

Amplituhedra, Cluster Algebras, and Positive Geometry Conference
May 30, 2024
Speaker: Melissa Sherman-Bennett, MIT & UC Davis
Title: Cluster algebras and tilings of amplituhedra
Abstract: Physicists Arkani-Hamed and Trnka introduced the amplituhedron to better understand scattering amplitudes in N=4 super Yang-Mills theory. The amplituhedron is the image of the totally nonnegative Grassmannian under the “amplituhedron map”. Examples of amplituhedra include cyclic polytopes, the totally nonnegative Grassmannian itself, and cyclic hyperplane arrangements. Of primary interest to physics are tilings of amplituhedra, which are roughly analogous to subdivisions of polytopes. I will discuss joint work with Even-Zohar, Lakrec, Parisi, Tessler and Williams on BCFW tilings of m=4 amplituhedra and the surprising connection between these tilings and the cluster algebra structure of the Grassmannian.