Seminar talk, 9 December 2009

In this talk I will review some aspects of the inverse problem of the calculus of variations, describing some open problems. More in detail, the topics of the seminar will be:

1 - Brief history and formulation of the problem in geometric terms;

2 - On different formulations of Helmholtz conditions and their uniqueness;

3 - On the invariant inverse problem, main results.

If time permits, the problem of finding minimal order Lagrangians for a given Euler-Lagrange equation will be discussed too.