# Manchester Geometry Seminar 2012/2013

**Thursday 15 November 2012. ** *The Frank Adams Room (Room 1.212), the Alan Turing Building. 4.15pm*
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On the Discrete Variational Calculus (a Gentle Introduction and Overview)

Elizabeth Mansfield (University of Kent)

`e.l.mansfield@kent.ac.uk`

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.