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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.
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