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

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

Lectures take place at the Independent University of Moscow on Wednesday evenings from 17:30 to 19:10 in room 308

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 1 (8 February 2012)

• Lecture 2 (15 February 2012)

• Lecture 3 (22 February 2012)

• Lecture 4 (29 February 2012)

• Lecture 5 (14 March 2012)

• Lecture 6 (21 March 2012)

• Lecture 7 (25 April 2012)

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