Žiga Krajnik: (Integrable) G-invariant Matrix Models in Discrete Space-Time

We define and study an integrable G-invariant dynamics of a field subject to a nonlinear constraint on a 1+1 dimensional discrete space-time lattice. The model allows for efficient numerical simulations, which suggest superdiffusion and Kardar-Parisi-Zhang physics in the entire family of models (arXiv:2003.05957). Further, I will present some recent results on extending the model onto other symmetric spaces and more general symmetry groups. Lastly I will discuss a recent surprising observation of conic sections in the correlation tensor of (non)-integrable G-invariant models of Landau-Lifshitz type.