Automorphisms of groups and limit elements

我学习了区间交换变换组，IET。在与Guirardel和Dahmani的联合工作中，我们证明了许多新的结果，包括IET中与李群同构的任何子群都是阿贝尔的。这是一个出乎意料的结果。我还研究了Teichmuller空间上的Funk度量，得到了一些有趣的结果。本文的研究表明了Teichmuller空间上的Funk度规与欧几里德空间中凸域上的Funk度规有很大的不同，为负曲率空间上的Funk度规的研究开辟了一个新的方向。

I studied the group of interval exchange transformations, IET. In a joint work with Guirardel and Dahmani, we proved many new results including that any subgroup in IET that is isomorphic to a Lie group is abelian. This is an unexpected result. I also studied the Funk metric on Teichmuller space, and obtained a number of interesting results. My study shows that the Funk metric on Teichmuller space is very different from the original Funk metric for a convex domain in a Euclidean space, and opened a new direction of the study on the Funk metric on a space which has negative curvature.