Poisson structures and cluster algebras

Speaker： Professor Jiang-Hua Lu（The University of Hong Kong）

Venue： 数学科学学院2楼报告厅(海纳苑2幢210室)

Abstract： After briefly introducing some basic facts in Poisson geometry, we explain how Poisson geometric considerations naturally lead to cluster mutations as in the theory of cluster algebras. As a special class of examples, we show how the so-called standard Poisson structure on generalized Schubert cells can be used, via the theory of symmetric Poisson CGL extensions developed by K. Goodearl and M. Yakimov, to obtain cluster structures on related varieties from Lie theory.