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Scope of the Abel Symposium, 2008

The Symposium will concern the theory of differential equations and its applications in geometry, mechanics and mathematical physics. Based on the mathematical heritage of Abel we are going to emphasise the role of algebro-geometric methods in the study of differential equations and mathematical physics. Ideas of symmetry and invariance, which lie at the core of Lie's theory, permeate all mathematical models in natural and engineering sciences. The most important topics include:
  • Algebraic and geometric methods in integrability of linear and non-linear differential equations,
  • Geometric analysis of the solutions and moduli spaces,
  • Role of symmetries, conservation laws, differential invariants and their generalizations,
  • Applications to geometric structures and their Lie equations,
  • Evolution equations and non-linear dynamics on the solution spaces,
  • Structures on equations and the global behavior of solutions,
  • Hamiltonian and Celestial mechanics,
  • Differential equations arising in field theories and quantum physics.