Seminar

In a joint work with Thomas Lam we use a deformation of Serre relations to define a family of Lie groups acting on planar electrical networks. In this talk I will explain how coordinate rings of those groups can be naturally endowed with Laurent phenomenon algebra structures. A combinatorial model for certain seeds of those algebras in terms of wiring diagrams has been studied by Henriques and Speyer under the name multidimensional cube recurrence. Our machinery of Laurent phenomenon algebras allows to extend this dynamics beyond the part modeled by wiring diagrams.