Talk information

Date: Sunday, June 30, 2024
Time: 10:10–11:00
Place: Schreiber 309
Speaker: Chaim Even-Zohar (Technion)
Title: BCFW Tilings and Cluster Algebras for the Amplituhedron

Abstract:

The amplituhedron $A(n,k,m)$ is a geometric object that encodes scattering amplitudes in various quantum field theories, discovered in 2013 by Arkani-Hamed and Trnka. One of the central conjectures has been that the amplituhedron $A(n,k,4)$ can be tiled by certain injective images of faces of the nonnegative Grassmannian $Gr+(k,n)$, which arise from an application of the BCFW recurrence. It has also been conjectured that each resulting tile and its facets can be characterized using compatible cluster variables for $Gr(4,n)$. In the talk, I will define the amplituhedron and outline our proof of the tiling conjecture, and shortly discuss our solution to the cluster adjacency conjecture.

Based on joint works with Tsviqa Lakrec, Matteo Parisi, Ran Tessler, Melissa Sherman-Bennett, and Lauren Williams.