Peter Hydon is giving a Mathematics Colloquium talk at the University of Glasgow today, Friday 10th October. His talk is on “Conservation laws: from differential to difference“. Famously, Noether’s (First) Theorem uses symmetries of a variational problem to generate conservation laws of the corresponding Euler-Lagrange equations. It is less well-known that one can construct conservation laws directly, for a given system of PDEs in Kovalevskaya form, whether or not it stems from a variational problem. In his colloquium talk, Peter describes how both of these approaches can be used (with appropriate modification) to find conservation laws of partial difference equations. He will also discuss a difference analogue of Noether’s Second Theorem, together with a new intermediate result that links Noether’s First and Second Theorems. These results open up some new ways to obtain finite difference approximations that preserve particular conservation laws and generalized Bianchi identities. The link to the School of Mathematics and Statistics at Glasgow is here.