250122 VO Selected topics in Differential Equations: Lie-Transformation Groups (2015S)

The lecture course will start out by providing a general introduction to the theory of Lie transformation groups. Based on this, our main topic will be the symmetry group analysis of differential equations. In this field, methods of the theory of Lie transformation groups are applied to the analysis of symmetry- and invariance properties of systems of partial differential equations. Sophus Lie himself was primarily motivated by such questions when he originally developed his theory of Lie groups. In addition we will also discuss symmetries of variational problems, a theory founded by Emmy Noether, which, in the form of the celebrated Noether theorems, has had a far-reaching impact on various branches of theoretical physics.

Prerequisites: Differential geometry 1, Lie groups (in the form of the standard courses offered at our Faculty).