**11/20, no lecture**

1. Background & Purposes

General Relativity models space-time by a Lorentzian manifold, whose metric evolves nonlinearly. Analysis of its solutions necessarily combines methods from both geometry and partial differential equations. In recent years this point of view has seen much success also in the study of other geometric wave equations. This course will expose students to many (though necessarily only a sample) of the ideas in mathematical relativity, with focus more on geometric aspects. The lecturer anticipates opening a course in the spring focusing on more analytic aspects of the theory.

2. Outline & Descriptions

Below is a tentative, chronological list of topics to be covered:

1. "What is General Relativity"?

2. Geodesics in GR (compared and contrasted with Riemannian geometry)

3. Geometry of null curves and null hypersurfaces

4. Causal structure

5. The Hawking-Penrose singularity theorems

6. A primer on Black Holes

7. The initial value problem and the wave-like nature of GR

**Time permitting, some rigidity results in GR will also be discussed.

3. Registration

https://forms.gle/K2uFnyjPwjnZqNjdA

4. Online Meeting Link

https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=m4a6405e25d947c56789ac5fc4d0822b0

5. Course Video

https://youtube.com/playlist?list=PLQZfZKhc0kiA5SJ3YdQpuky9jo1K6y7T6&si=IjU3VXv-xGICQ-3I

6. Course Note

*Already sent to the participants, please contact Murphy <murphyyu@ncts.tw> if you need any assistance.