The last decade witnessed intense efforts to realize zero-energy Majorana modes in topological superconductors. Most of the experimental observations relied on conductance measurements and spectroscopy, which, however, are not sufficient to unveil the non-local nature of these exotic quasiparticles. In this talk I will discuss a transport phenomenon, the topological Kondo effect, that can provide more direct evidence of the non-locality of Majorana modes. The study of this phenomenon beyond the renormalization group predictions is challenging. To obtain quantitative indications of its onset, I will first discuss possible physical implementations of this phenomenon and then present the matrix-product-state simulations of the dynamics of superconductor-seminductor hybrid systems aiming at realizing this peculiar transport phenomenon. Our simulations of quantum quenches, in particular, allow us to determine the topological Kondo temperature that characterizes the emergence of this effect and to discuss realistic conditions to observe its peculiar fractional conductance.
