MATH6021 - Topics in Geometry I - 2020/21

General Information

Lecturer

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

Time and Venue

• Lecture: Mon 9:30am-12:15pm online via ZOOM

Course Description

This is a graduate level topics course on geometry. This term we will focus on the theory of minimal surfaces and their applications. After discussing some foundations like first and second variation formula, Bernstein theorems and curvature estimates, we will discuss the existence and regularity theory for minimal surfaces. Depending on the time available, we will also cover the geometric applications and some recent developments on the min-max theory for minimal surfaces. The goal is to understand the analytic and geometric aspects of minimal surfaces and their applications in global geometry and topology. We shall assume as prerequisite a solid understanding of Riemannian Geometry (at the level of MATH5061), as well as a working knowledge on partial differential equations (at the level of MATH5022) and real analysis (at the level of MATH5011).

Textbooks

• "A Course in Minimal Surfaces", by Tobias Colding and William Minicozzi II, AMS Graduate Studies in Mathematics Vol. 121

Pre-class Notes

• Course outline
• Presentations and Essays

Lecture Notes

• Lecture 1 on Sep 7
• Lecture 2 on Sep 14
• Lecture 3 on Sep 21
• Lecture 4 on Sep 28
• Lecture 5 on Oct 5
• Lecture 6 on Oct 12
• Lecture 7 on Oct 19
• Lecture 8 on Nov 2
• Lecture 9 on Nov 9
• Lecture 10 on Nov 16
• Lecture 11 on Nov 23
• Lecture 12 on Nov 30

Assessment Scheme

Honesty in Academic Work

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