In the course we will first introduce Geometric analysis techniques and various important applications from the basic. If time allows we would also like to discuss some recent developments in minimal submanifolds general relativity and Min-Max theory.

The content of the course will heavily depend on the background of the students who take the class. Students that are interested in the class, please email me or talk to me by Aug. 31 so I can modify the arrangement accordingly to students' need. In case this is the first course of Geometric Analysis for students in the class, we will mainly follow Peter Li's "Lecture Notes on Geometric Analysis", plus some related papers or material from "Lectures on Differential Geometry" by Schoen and Yau. We will focus more on recent work or papers if students have more background. Some material will be assigned to students to study and present.