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

  1. Introduction
  2. Differential calculus over commutative algebras
  3. Geometry of jets and nonlinear differential equations
  4. Symmetries
  5. Coverings and nonlocal symmetries
  6. Froelicher-Nijenhuis brackets and algebras with flat connections
  7. Deformations of differential equations
  8. Recursion operators
  9. C-differential calculus
  10. Generalities of homological algebra. Spectral sequences
  11. Horizontal cohomology of differential equations
  12. Algebraic model for Lagrangian formalism
  13. Compatibility complex
  14. Vinogradov's C-spectral sequence of jet bundles and differential equations
  15. Calculus of variations over infinite prolongations
  16. Conservation laws
  17. Noether theorems
  18. Hamiltonian methods for evolution differential equations
  19. Differential super-equations
  20. Antifield-BRST formalism
Lecture notes of the course: The Diffiety Inst. Preprint Series, DIPS 7/98.
Open Education and Sciences
Dr. Roman Strzondala
P. O. Box 84
746 20 Opava 1, Czech Republic