Alexander Verbovetsky's Introductory lectures on the Geometry of Differential Equations

Spring 2012

Short syllabus

• The Vinogradov spectral sequence

• Conservation laws

• Lagrangian formalism. Noether's theorem

• Tangent and cotangent coverings over equations

• Schouten bracket and Hamiltonian structures. Bi-Hamiltonian equations

Recommended literature

• A. V. Bocharov, A. M. Verbovetsky, A. M. Vinogradov (editor), S. V. Duzhin, I. S. Krasil'shchik (editor), A. V. Samokhin, Yu. N. Torkhov, N. G. Khor'kova, and V. N. Chetverikov Simmetrii i zakony sokhraneniya uravnenij matematicheskoj fiziki, Factorial, Moscow, 2nd edition, 2005. (English translation: Symmetries and conservation laws for differential equations of mathematical physics, AMS, 1999.)

• Joseph Krasil'shchik and Alexander Verbovetsky, Geometry of jet spaces and integrable systems, J. Geom. Phys. 61 (2011), 1633-1674, arXiv:1002.0077