There is a recent breakthrough paper
The Amplituhedron BCFW Triangulation by Chaim Even-Zohar, Tsviqa Lakrec, and Ran Tessler
Abstract: The amplituhedron is a geometric object, introduced by Arkani-Hamed and Trnka (2013) in the study of scattering amplitudes in quantum field theories. They conjecture that admits a decomposition into images of BCFW positroid cells, arising from the Britto–Cachazo–Feng–Witten recurrence (2005). We prove that this conjecture is true.
Congratulations to Chaim, Tsviqa, and Ran!
- The introduction to the paper give a very friendly introduction of the topic as well as a variety of results between 2013 and today.
- Ran Tessler gave recently a lovely colloquium talk about the result in Tel Aviv University, here are the slides.
- For a 2015 post about these objects and some thoughts about the combinatorial side: The Simplex, the Cyclic polytope, the Positroidron, the Amplituhedron, and Beyond. See also this post for a related lecture series by Alexander Postnikov. (Here are quite a few blog posts on the physics side from “4-gravitons”.)
(Click for a larger image.) Questions that arise naturally:
Is there an analog for the “moment curve”? Are there analogs for “neighborly polytopes”?
Do amplituhedra maximize numbers of cells or related parameters like the cyclic polytopes do?
Are they amplituhedra “universal” objects like vertices of the cyclic polytopes?