ICTS

Symmetries play an important role in differential equations both in their qualitative and quantitative study. The classical symmetries introduced by Lie, and employed by Noether, often require specific domains for the differential equations. This creates difficulty in adapting symmetry based methods when solving boundary-value problems for PDEs. In this talk, I'll introduce an alternative symmetry-based approach that handles boundary-value problems with equal ease. These symmetries are much closer to the those originally considered by Galois. Time permitting, I will mention connections to integrable systems.