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Lie systems: theory, generalizations, applications

22.09.2014 -  27.09.2014 | Warsaw



The subject of the mini-workshop is closely related to the grant HARMONIA, devoted to a cooperation with Spain in this field. The theory of Lie systems analyses a class of systems of first-order ordinary differential equations, the so-called Lie systems, general solutions of which can be described in terms of a generic finite family of particular solutions and a set of constans, by a certain function, the superposition rule. Their interesting geometric features give rise to important tools and have originated new mathematical techniques and notions used for investigating differential equations.

The programme of the workshop will focus on the study of Lie systems, their generalizations, and applications in both mathematics and physics. In addition, the programme includes the analysis of problems related to symplectic and Poisson geometry, quantum mechanics and supergeometry. More specifically, the research group will work on:

  • Lie-Hamilton systems;
  • Lie symmetries, Lax pairs and the PainlevĂ© property;
  • Quasi-Lie systems and their applications;
  • Geometry of differential equations on supermanifolds;
  • Dirac-Lie systems;
  • Lie systems on k-symplectic manifolds;
  • Lie systems on Riemannian manifolds;
  • Lie systems on algebroids.