Last updated May 12, 2000
Introduction to the geometry of jet spaces and differential equations.
A course program (preliminary):
Jets of submanifolds
Differential group
Affine structures in jet bundles
Lie transformations, Lie-Baecklund theorem
Classification of integral manifolds
Geometrical singularities of solutions of PDEs
Characteristics of distribution and the theory of one first order equation
Cartan distribution on equations
Extrinsic and intrinsic geometry
Symmetries, distributions, and integration of ordinary equations
Characteristic classes of multi-valued solutions of systems of nonlinear PDEs
Theory of solvability, formal integrability, involutiveness, Cartan-Kahler theorem, symbols, compatibility complexes