Speaker:  Lauren Williams (Harvard University)

Title:  Cluster algebras and tilings for the m = 4 amplituhedron

Abstract:  The amplituhedron A_n,k,m(Z) is the image of the positive Grassmannian under a map induced by a positive linear map. It was originally introduced in physics by Arkani Hamed and Trnka in order to give a geometric interpretation of scattering amplitudes and in particular the Britto-Cachazo Feng-Witten recurrence. The amplituhedron has since been linked to cluster algebras and interesting objects from combinatorics. I will give an introduction to the amplituhedron and discuss our recent proof of the cluster adjacency conjecture for BCFW tiles, as well as the BCFW tiling conjecture. Based on joint work with Even-Zohar, Lakrec, Parisi, Sherman-Bennett, and Tessler.