Alexander Verbovetsky's Introductory lectures on the 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 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)

• Lecture 8 (2 May 2012) is missing

• Lecture 9 (16 May 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

Recommended literature

• Joseph Krasil'shchik in collaboration with Barbara Prinari, Lectures on linear differential operators over commutative algebras. (The 1st Italian diffiety school, July, 1998), Diffiety Inst. Preprint Series 1 (1999), DIPS 1/99, local copy.