Integrability of Lie systems and some of its applications in physics
  The geometric theory of Lie systems will be used to establish integrability conditions for several systems of differential equations, in particular Riccati equations and Ermakov systems. Many different integrability criteria in the literature will be analyzed from this new perspective and some applications in physics will be given. 
Jos\'e F. Cari\~nena, Javier de Lucas and Manuel F. Ra\~nada