Paul Heslop - The (loop) amplituhedron, squared amplituhedron and correlahedron.

This lecture was part of the Thematic Programme on "Amplitudes and Algebraic Geometry" held at the ESI February 19 - March 27, 2026.

Correlation functions of half BPS operators are key quantities in N=4 SYM with a very close unifying relation to amplitudes (several different amplitude integrands arise out of the same correlator). The correlahedron is a corresponding geometric object, proposed in 2017 with Eden and Mason, with a very simple mathematical description, similar to the loop amplituhedron. I will discuss the arguments leading to the correlahedron as well as several developments since then with Dian and Stewart and in progress. In particular I will discuss subtleties of positive geometry, relevant even for the loop amplituhedron, a dual description of the correlahedron, the relation to recent work of He, Huang and Kuo which has verified the correlahedron geometry at 4 points, 4 loops and extension beyond 4 points.

Видео Paul Heslop - The (loop) amplituhedron, squared amplituhedron and correlahedron. канала Erwin Schrödinger International Institute for Mathematics and Physics (ESI)