10 Sep 2008; Mat-Nat Faculty (UiTø), room A228. Wednesday 10:15-12:00
"Point classification of 2nd order ODEs: Tresse classification revisited and beyond".
2nd order ODEs are the simplest, yet among most widespread in the models types of differential equations. Most explicit integration methods for second order ODEs are related to the action of the point transformations pseudogroup. In 1896 Tresse (French student of Sophus Lie) gave a complete description of relative differential invariants for this problem and thus solved the equivalence problem. This problem was considered in the papers of many known mathematicians, both before (e.g. Lie, Liouville and Darboux) and after (e.g. Cartan, Fefferman and Arnold) the manuscript I'd like to discuss.
I will give a detailed historical account of the progress on the problem and then recast this into the modern language. Some new results will be briefly discussed as well. If time permits, I will also mention some of related problems, still pending the solution.