Séminaire Lotharingien de Combinatoire, 89B.47 (2023), 12 pp.

Chaim Even-Zohar, Tsviqa Lakrec and Ran J. Tessler

The BCFW Tiling of the Amplituhedron

Abstract. The amplituhedron A_n,k,4 is a geometric object, discovered by Arkani-Hamed and Trnka (2013) in the study of scattering amplitudes in quantum field theories. They conjecture that A_n,k,4 admits a decomposition into tiles, which is based on a certain combinatorial structure. The tiles are images of BCFW positroid cells in the nonnegative Grassmannian Gr_k,n^≥ that arise from the Britto-Cachazo-Feng-Witten recurrence (2005).

In a recent preprint we prove this conjecture. The full paper is available online at https://arxiv.org/pdf/2112.02703. In this extended abstract we review the amplituhedron and its BCFW tiling, and outline the main ideas from the proof.

Received: November 15, 2022. Accepted: February 20, 2023. Final version: April 1, 2023.

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