Joseph Krasil'shchik's lectures on the linear differential operators over commutative algebras and geometry of jet spaces: Difference between revisions

Revision as of 13:43, 17 September 2015

Autumn 2015

Lectures will take place at the Independent University of Moscow on Wednesday evenings in room 303 from 17:30 to 19:10

The first lecture will meet on 9 September

Categories and functors (introduction).
Linear differential operators with values in modules. Main properties.
Derivations.
Representative objects: jets and differential forms.
Differential calculus over commutative algebras.
Schouten-Nijenhuis brackets and related cohomologies. Algebraic model of Hamiltonian formalism.
Frölicher-Nijenhuis brackets and related cohomologies. Algebraic model of nonlinear differential equations.
Geometric realization. Relation between the category of vector bundles over a manifold and the category of projective modules over a commutative ring.
Jets of locally trivial bundles over smooth manifolds. The Cartan distribution.
Symmetries of the Cartan distribution and the Lie-Bäcklund theorem.
Differential equations as geometric objects and their symmetries.
Symmetries of ordinary equations and Lie-Bianchi theorem on the integration by quadratures.

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	* [http://video.gdeq.net/GDEq-lec-20150909.mp4 Lecture 1 (9 September 2015)]		* [http://video.gdeq.net/GDEq-lec-20150909.mp4 Lecture 1 (9 September 2015)]

	[[Category:Lectures\|Krasil'shchik]]		[[Category:Lectures\|Krasil'shchik 7984a]]