Manchester Geometry Seminar 2012/2013

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:

• other discrete variational complexes;
• creation of global lattice-like manifolds, where "adjacency" replaces topology;
• obtaining the difference analogue of the preserved symplectic form and the Hilbert integral.

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.