Advanced 5-day course Homological methods in equations of
mathematical physics
17-21 August 1998, Levoca, Slovakia
Lecturers:
Joseph Krasil'shchik
and Alexander Verbovetsky
The course is aimed to mathematicians and theoretical physicists on
post-doctoral level, working in differential equations, mathematical
physics, and differential geometry.
Participants are supposed to be familiar with basic concepts of
classical analysis, differential manifolds, and tensor calculus.
Program of the course
Introduction
Differential calculus over commutative algebras
Geometry of jets and nonlinear differential equations
Symmetries
Coverings and nonlocal symmetries
Froelicher-Nijenhuis brackets and algebras with flat connections
Deformations of differential equations
Recursion operators
C-differential calculus
Generalities of homological algebra. Spectral sequences
Horizontal cohomology of differential equations
Algebraic model for Lagrangian formalism
Compatibility complex
Vinogradov's C-spectral sequence of jet bundles and differential
equations
Calculus of variations over infinite prolongations
Conservation laws
Noether theorems
Hamiltonian methods for evolution differential equations