6 points, SCA Band 2, 0.125 EFTSL
Postgraduate - Unit
Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.
Faculty
Organisational Unit
School of Mathematical Sciences
Chief examiner(s)
Coordinator(s)
Not offered in 2019
Notes
This unit is offered in alternate years commencing S2, 2020
Synopsis
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.
Outcomes
On completion of this unit students will be able to:
- Apply sophisticated tools of mathematical analysis to understand manifolds in a variety of settings
- Demonstrate a profound understanding of connections between the geometry of a manifold, and the analytic properties of the manifold.
- Communicate complex information and results with clarity.
Assessment
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.
Workload requirements
- 3 hours of lectures
- 1-hour tutorial and
- 8 hours of independent study per week
See also Unit timetable information
This unit applies to the following area(s) of study
Master of Mathematics