2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139496Rational conformal field theories produce a tower of finite-dimensional representations of surface mapping class groups, acting on the conformal blocks of the theory. We review this formalism. We show that many recent mathematical developments can be fit into the first 2 floors of this tower. We also review what is known in higher genus.17 pages; conference proceedings Number theory and physicsQuantum AlgebraNumber Theory81T40; 32G15, 81T45, 32G81text