Xiaodong Wang, a Professor in Electrical Engineering Department，Columbia University.Research interests: Statistical signal processing Genomic signal processing ,Bioinformatics Communication theory, Wireless communications, Optical communications.
Mostow’s strong rigidity theorem for locally symmetric spaces is a famous result in geometry. In the real hyperbolic case it asserts that two compact hyperbolic manifolds of dimension at least three with isomorphic fundamental groups must be isometric. In this topic course we will study the geometry of negatively curved manifolds. We will start with a review of Riemannian geometry, especially the Rauch comparison theorem. Then we will develop the various concepts and techniques in the subject. Our ultimate goal is to prove a deep theorem of Besson-Courtois-Gallot on volume entropy. As a simple corollary, we obtain the Mostow strong rigidity in all the rank one cases in a unified way.