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 brackets 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.)