Last updated May 12, 2000
Introduction to the geometry of jet spaces and differential equations.
A course program (preliminary):

  1. Jets of submanifolds
  2. Differential group
  3. Affine structures in jet bundles
  4. Lie transformations, Lie-Baecklund theorem
  5. Classification of integral manifolds
  6. Geometrical singularities of solutions of PDEs
  7. Characteristics of distribution and the theory of one first order equation
  8. Cartan distribution on equations
  9. Extrinsic and intrinsic geometry
  10. Symmetries, distributions, and integration of ordinary equations
  11. Characteristic classes of multi-valued solutions of systems of nonlinear PDEs
  12. Theory of solvability, formal integrability, involutiveness, Cartan-Kahler theorem, symbols, compatibility complexes