本项目主要研究可积系统及其在几何物理中的一些应用，这是当前数学物理研究领域中的一个热点课题。具体的说，我们不仅关注可积系统理论的内在发展，如超对称化、离散化、对称性、Hamiltonian结构和双Hamiltonian 约化等；同时在此基础上更多的关注与之相关的若干专题，如Frobenius流形、无限维（超）Lie群上的测地流方程和广义的Euler-Ponicare系统、可交换的微分算子的构造等。

In this project, we shall discuss some applications of integrable systems, which is an increasing interested topic. More precisely, on the one hand, we hope to understand more symmetries and Hamiltonian structures of some (super-) integrable systems. On the other hand, we are interested in several topics related to integrable systems, including Frobenius manifolds, geodesic flow equations and generalized Euler-Poincare systems on infinite-dimensional (super-) Lie groups and commutative differential operators,etc.