U-Equations from Finite Dimensional Algebras - Applications in Cluster Algebras and Amplitudes

Watch a 51-minute conference talk from the Amplituhedra, Cluster Algebras, and Positive Geometry Conference where Hugh Thomas from Université du Québec à Montréal explores the system of u-equations associated with finite dimensional algebras. Learn how these equations generalize the 1969 Koba-Nielsen system through the lens of Dynkin type A quiver representation theory. Discover key features of solution spaces, including connections to tau-tilting theory and relationships between different solution spaces. Explore how various finite-dimensional algebra choices relate to cluster algebras, Grassmannian combinatorics of non-kissing complexes, and curves-on-surfaces models relevant to amplitudes. The presentation covers collaborative research with Nima Arkani-Hamed, Hadleigh Frost, Pierre-Guy Plamondon, and Giulio Salvatori.