The 3rd summer school on geometry of differential equations

Organized by the Mathematical Institute of Silesian University in Opava, the school is the third in a series supported by the European Social Fund under the project CZ.1.07/2.3.00/20.0002.

Scientific Programme

Two courses will take place during the summer school.

Differential Invariants

V.V. Lychagin (University of Troms\o, Troms\o, Norway)

• Invariants in Algebra, Geometry and Analysis.
• Actions of algebraic Lie groups and Lie algebras. Polynomial and rational invariants. Geometrical and categorical factors. Hilbert and Rosenlicht theorems.
• Geometry of jet spaces and PDEs. Algebraic structures on PDEs. Algebraic PDEs.
• Jets of diffeomorphisms and Lie algebraic pseudogroups, their actions on PDEs.
• Polynomial and rational differential invariants. Lie--Tresse theorem.
• Differential syzygies and factor equations.
• Various methods for computation differential invariants: computer, moving frames, connections.
• Applications:
  • Algebra: differential contra algebraic invariants; differential invariants in algebraic problems.
  • Geometry: Klein geometries and invariants of geometrical quantities, Riemann and Einstein manifolds, etc.
  • Analysis: Differential invariants for ODEs (Tresse and Wilczy\'{n}ski invariants),

contact differential invariants for Monge--Amp\`ere equations, projective and conformal invariants in neurogeometry and image recognition.