THE RUSSIAN WINTER 2001 SCHOOL
Last updated October 9, 2003
This school was organizing in cooperation with the Pereslavl State University and took place in Pereslavl'-Zalessky from January 26 till February 5, 2001

The program of the school:
  1. Smooth manifolds. Vector fields. Differential forms. Distributions. Relation to commutative algebra.
  2. Geometry of ordinary equations. Symmetries. Applications of symmetries to solving ODEs. Lie-Bianchi theorem on integration of ODEs by quadratures.
  3. Contact geometry and the theory of first-order equations. Relation to symplectic geometry and Hamiltonian mechanics.
  4. Finite jets of submanifolds. Cartan distribution. Integral manifolds. Lie-Baeklund theorem.
  5. Differential equations as geometric objects. Theory of symmetries. Application of symmetries (invariant solutions, reproduction of solutions, factorization). Examples. External and internal geometry of equations.
  6. Infinite jets. Algebraic formalism. Prolongation of differential equations. Higher symmetries and their computation. Examples. Computer methods for finding symmetries.
  7. Conservation laws and their computation. Noether theorem. Hamiltonian structures. Examples.
  8. Coverings over differential equations and nonlocal symmetries. Baeklund transformations.
Questions and suggestions should go to Jet Nestruev, jet @ diffiety.ac.ru.