Report Title：Dirac-Lie systems of differential equations

Reporter： Janusz Grabowski

Affiliated unit：Polish Academy of Sciences

Report time：October 24, 16:50-17:50

Report Location: Room 209, Zhengxin Building, Jilin University

Report Abstract: Sophus Lie proved a theorem about nonlinear superposition rules for solutions of some non-autonomous systems of nonlinear ordinary differential equations. These systems can be considered as a generalization of linear systems, as they admit a superposition rule, allowing us to express the general solution of the system by means of a superposition function in terms of a set of fundamental particular solutions, in which the superposition rule is possibly no longer a linear function. Such systems are nowadays called Lie systems. More specific Lie systems have also been studied, e.g., in connection with symplectic or Poisson geometry.

We will discuss Lie systems from a geometric perspective, presenting the fundamental result of Lie in the modern setting, including Dirac structures into the picture. The talk will be illustrated by meny examples.

Presenter Introduction： Professor Janusz Grabowski is the Head of the Department of Mathematical Physics and Differential Geometry in the Institute of Mathematics, Polish Academy of Sciences. His main interests are differential geometry and mathematical physics. He published fundamental results on Lie algebras of vector fields, diffeomorhism groups, Lie systems, Poisson and Jacobi manifolds, Lie groupoids and algebroids, Lagrangian and Hamiltonian mechanics (including mechanics on contact manifolds), supergeometry, geometry of quantum states and entanglement, etc.