Rigidity of Teichmueller space
Loosely speaking, Holomorphic rigidity of Teichmueller space states that the action of mapping class group uniquely determines the Teichmueller space as a complex manifold. I will sketch the main ideas involved in proving such result. The method of proof is through harmonic maps and fits into the framework of geometric superrigidity. In addition, I may discuss a harmonic maps proof of both the high rank and the rank one superrigidity of the mapping class group proved via other methods by Farb-Masur and Yeung.
