22 Sep 2005; Mat-Nat Faculty (UITO), room U6=C321. Thursday 10:15-12:00

Boris Kruglikov "Multi-brackets of differential operators and compatibility of PDEs - 1".

In this talk I will describe a new approach to check compatibility of the systems of PDEs.
It is based on the geometry of PDEs, Spencer cohomology theory and abstract commutative algebra.
Two important applications will be discussed:

1. Solvability of the systems of PDEs. Even with linear PDEs this is a very non-trivial question.

2. Construction of auxiliary integrals and integration of PDEs. For evolutionary PDEs this is related to the method discussed in the talk of myself and Valentin

The work is joint with V. Lychagin.