Joseph Krasil'shchik's introductory lectures on the Geometry of Differential Equations

Lectures take place in the Independent University of Moscow on Wednesdays at 17:30 in room 211

Short syllabus

• Jets of bundles
  The Cartan distribution
  Symmetries of the Cartan distribution
  The Lie-Bäcklund theorem

• Nonlinear differential equations and operators
  Classical symmetries of differential equations, their computation and application
  The Bianci-Lie theorem

• Infinite jets and geometric structures on them
  The Cartan distribution on infinite jets and its symmetries
  Linearizations and evolutionary vector fields

• Prolongations of differential equations
  Infinitely prolonged equations
  Higher symmetries of differential equations, their computation and application
  Recursion operators for symmetries