Mini-Workshop: Scattering Amplitudes, Cluster Algebras, and Positive Geometries

Abstract

Cluster algebras were developed by Fomin and Zelevinsky about twenty years ago. While the initial motivation came from within algebra (total positivity, canonical bases), it quickly became clear that cluster algebras possess deep links to a host of other subjects in mathematics and physics. In a separate vein, starting about ten years ago, Arkani-Hamed and his collaborators began a program of reformulating the bases of quantum field theory, motivated by a desire to discover the basic rules of quantum mechanics and spacetime as arising from deeper mathematical principles. Their approach to the fundamental problem of particle scattering amplitudes entails encoding the solution in geometrical objects, “positive geometries” and “amplituhedra”. Surprisingly, cluster algebras have been found to be tightly woven into the mathematics needed to describe these geometries. The purpose of this workshop is to explore the various connections between cluster algebras, scattering amplitudes, and positive geometries.