Seminar talk, 9 November 2011

Speaker: Stanislav Minkov

Title: A new proof of Lie's theorem on overdetermined systems after a work by Boris Kruglikov

Abstract:
The talk will discuss a classical result by Lie on overdetermined systems of PDEs, which under some conditions locally can be reduced to ODEs. A new proof by B.Kruglikov [1] is based on "geometric considerations", namely jets, the Spencer homology, and the characteristic method. Using the new technique the author extends the theorem by considering the conditions of integrability of the system and integration in closed form. For this end the author uses all machinery (the Darboux integrability and the flags) introduced on the previous seminar by Joseph Krasil'shchik. The author also announces his results about generalisation of the Laplace transformations [2], on which I will try to tell as well.

References:
[1] Boris Kruglikov, Lie theorem via rank 2 distributions (integration of PDE of class $\omega =1$), arXiv:1108.5854

[2] Boris Kruglikov, Laplace transformation of Lie class $\omega =1$ overdetermined systems, arXiv:1108.5852