A Lie groupoid and algebroid approach to partial differential equations

In this talk, we present how the theory of Lie groupoids and Lie algebroids can be applied to describe the geometric formalism of ordinary and partial differential equations in an elegant and clarifying way. In particular, we employ Lie groupoids and algebroids to characterise flows of ordinary differential equations and Lie symmetries of partial differential equations. Advanced results in the theory of Lie algebroids and groupoids — such as the integration of Lie algebroids — enable us to deal with the locality of certain structures arising in differential equations in a natural, global, and manageable manner. The theory will be illustrated with several examples motivated by physics.