Poisson geometry and some applications

The classical Poisson bracket was introduced by Poisson in 1809, which played a fundamental role in classical mechanics. The first nontrivial degenerate Poisson structure was discovered by Lie more than a century ago. The notion of Poisson manifolds in modern language was first introduced by Lichnerowicz in 1977. The subject of Poisson geometry has gone through rapid development in the past two decades due to its connection with physics and other areas of mathematics such as integrable systems, quantum groups and quantization. In this talk, I will give a brief survey of its recent development and particularly its application in quantization of dynamical r-matrices, which was rooted in conformal field theory.