题目: Ratner's measure classification theorem for semisimple groups

授课人：杨磊，四川大学

授课时间地点：4月14日（周三）19:00-21:00    管楼1318

                        4月15日 (周四)  14:00-15:35     5教5306

                        4月21日 (周三)  19:00-21:00     5教5306

                        4月22日 (周四)  14:00-15:35     5教5306

摘要: Ratner’s measure classification theorem is (arguably) the most important result in homogeneous dynamics. It has many important applications to number theory. Moreover, the fundamental ideas in her proof inspired many other significant progress in dynamical systems, including Lindenstrauss’s fields medal work on measure rigidity of higher rank diagonal action on homogeneous spaces, the work of Benoit and Quint on random walks on homogeneous spaces, and the work of Eskin and Mirzakhani on SL(2,R)-invariant measures on moduli spaces of hyperbolic surfaces. In this mini course, I will explain the proof of Ratner’s theorem when the ambient group is semisimple. In the first lecture, I will give a general introduction and some preliminary results on Lie groups and representations. The second lecture will be devoted to the proof of simpler case where the measure is invariant under the action of SL(2,R). In the third and fourth lectures, I will explain the proof of the general case. I will try to be self contained and explain as many details as possible.