Boris Kruglikov (joint with V. Lychagin) - "Algebraic aspects of compatibility of PDEs".

In this talk I explain algebraic aspects of the problem of computing compatibility conditions
for overdetermined systems of nonlinear partial differential equations.

In the case the symbolic modules are nice, the corresponding differential syzygies can be
represented as certain multi-brackets of differential operators (including Jacobi-Mayer bracket
for the scalar systems).

I will discuss how to compute compatibilites in the general case and in the presence of 
a pseudogroup of symmetries. Application to integrability schemes will be also mentioned.