MTH5121 - Analysis on manifolds - 2019

In this course, you will investigate manifolds using the tools of analysis. In this setting, curvature and topology become crucial. The topics covered may include Riemann surfaces, Lie derivatives, Hodge theory, spectral theory on manifolds, comparison theorems, topics in mathematical physics, and geometric differential equations such as the minimal surface equation, geometric evolution equations, and harmonic maps. You will also examine some foundational theorems in the field, such as the uniformisation theorem, the resolution of the Yamabe problem, or the positive mass theorem.

You will also learn, through guided self-reading, additional topics based on their specific background (what other analysis units - Partial differential equations, Measure theory, etc. - they have already taken).

On completion of this unit students will be able to:

1. Apply sophisticated tools of mathematical analysis to understand manifolds in a variety of settings.
2. Demonstrate a profound understanding of connections between the geometry of a manifold, and the analytic properties of the manifold.
3. Communicate complex information and results with clarity.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5121 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4121Not offered in 2019. The assignments and exam in this unit will use some common items from the MTH4121Not offered in 2019 assessment tasks, in combination with several higher level questions and tasks.

3 hours of lectures

1-hour tutorial and

10 hours of independent study per week

See also Unit timetable information

Master of Mathematics