The theory of Lie systems analyzes a class of systems of first-order ordinary differential equations, the so-called Lie systems, whose general solutions can be described in terms of a generic finite family of particular solutions and a set of constants, 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 program of our working group focused on the study of Lie systems, their generalizations, and applications in both, mathematics and physics. In addition, our plan entails the analysis of problems related to symplectic and Poisson geometry, quantum mechanics, and supergeometry. More specifically, we will work on:
— Lie-Hamilton systems.
— Lie symmetries, Lax pairs and the Painlevé 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.
Co-financed by:Warsaw Center of Mathematics and Computer Science
The Polish National Science Centre
grant under the contract number DEC-2012/04/M/ST1/00523