Elizabeth Mansfield (University of Kent)
I will discuss the formal finite difference variational calculus, showing the clear analogues with the smooth formal variational calculus. This presents the calculus as a chain complex (which will be described), and allows to solve questions such as, is some expression a total derivative, and if so, of what.
I will also discuss the analogues of Noether's first and second theorems. The first deals with conservation laws, the second with dependencies between the Euler-Lagrange equations.
Time permitting, I can discuss a choice of:
Most of the above is joint work with Peter Hydon (Surrey). I plan that the talk will be a gentle introduction suitable for graduate students and am happy to present or abandon topics according to taste.