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