MATH6022B - Topics in Geometry II - 2021/22

Announcement

• Due to the current COVID-19 situation, we will switch to 100% online teaching via ZOOM (effective from Jan 27) until further notice. The ZOOM meeting information will be sent to you via email. If you are not registered in the course but would like to attend to the online lectures, please contact me by email.

General Information

Lecturer

• LI Man-chun Martin
  • Office: LSB 236
  • Tel: 3943-1851
  • Email:
  • Office Hours: By appointment

Time and Venue

• Lecture: Thur 3:30-6:15PM at LSB 219

Course Description

This is a graduate level topics course on geometry. This term we will focus on the geometric aspects of mathematical general relativity. Many problems in general relativity are essentially geometric in nature, in the sense that they can be understood in terms of Riemannian geometry and partial differential equations. This course will be centered around the study of mass in general relativity using the techniques of geometric analysis. More specifically, we will give an overview of the positive mass theorem and other related results such as Penrose inequality, drawing on a variety of tools used in this area of research, including minimal hypersurfaces, conformal geometry, inverse mean curvature flow, conformal flow, spinors and the Dirac operator, marginally outer trapped surfaces, and density theorems. We shall assume as prerequisite a working understanding of Riemannian Geometry (at the level of MATH5061), as well as basic knowledge on elliptic partial differential equations (at the level of MATH5022). In particular, prior exposure to general relativity is helpful but not absolutely required.

Textbooks

• "Geometric Relativity" by Dan A. Lee, AMS Graduate Studies in Mathematics Vol. 201

Pre-class Notes

• Course outline
• Presentations and essays

Assessment Scheme

Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

and thereby help avoid any practice that would not be acceptable.