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

From Geometry of Differential Equations

Spring 2012 (continuation of Joseph Krasil'shchik's lectures)

## 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

## Video records of the lectures

*Via http://ium.mccme.ru/IUM-video.html*

- Lecture 8 (2 May 2012) is missing

## 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