# FELLESKOLLOKVIUM FREDAG 21. APRIL 2006

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Boris Kruglikov :

"Multi-brackets of differential operators and compatibility of PDEs."

I will discuss applications of methods from commutative algebra
and differential geometry to differential equations.
Namely, the Buchsbaum-Rim complex can be used to calculate a resolution
of the module corresponding to a system of linear differential equations of generalized
complete intersection type. This is further applied to overdetermined systems
of non-linear differential equations to calculate their Spencer delta-cohomology and
the curvature tensors that are obstructions to formal integrability.
These latter can be identified with certain multi-brackets, which yields an effective
compatibility criterion.

I will show how to apply the main result to generalize classical integrability
methods developed by Sophus Lie. I also explain how the compatibility
result can be used to solve some old problems in differential geometry:
Darboux problem on Liouville metrics, Blaschke web-conjecture and others.
The work is joint with V.Lychagin. Only basic knowledge from algebra and
geometry is required.

1430-1530 i pausearealet i 7. etage

Kaffe og kjeks fra kl 1400

EB/HB/BJ/PAØ Hovedsiden