Joseph Krasil'shchik's lectures on the linear differential operators over commutative algebras and geometry of jet spaces: Difference between revisions
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#Differential equations as geometric objects and their symmetries. | #Differential equations as geometric objects and their symmetries. | ||
#Symmetries of ordinary equations and Lie-Bianchi theorem on the integration by quadratures. | #Symmetries of ordinary equations and Lie-Bianchi theorem on the integration by quadratures. | ||
==Lecture notes and problems== | |||
[[Media:IUM-lectures-2015-09-17.pdf]] | |||
==Video records of the lectures== | ==Video records of the lectures== | ||
Revision as of 11:36, 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
Syllabus
- Category and functors (introduction).
- Linear differential operators with values in modules. Main properties.
- Derivations.
- Representative objects: jets and differential forms.
- Differential calculus over commutative algebras.
- Frölicher-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.
Lecture notes and problems
Media:IUM-lectures-2015-09-17.pdf
Video records of the lectures
Via http://ium.mccme.ru/IUM-video.html, Math-Net.Ru, and YouTube