Undergraduate Course: Modern Methods in Geometry and Topology (MATH11142)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Year 5 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | NB. This course is delivered *biennially* with the next instance being in 2026-27. It is anticipated that it would then be delivered every other session thereafter.
This course will highlight important developments in geometry and topology throughout the preceding century, and train students to approach problems in these fields with a modern perspective. Topics will draw from the research interests and expertise of staff teaching the course. |
| Course description |
Symplectic geometry is the study of manifolds equipped with a closed, nondegenerate two-form. It was invented to study classical mechanics, but has been re-invigorated and enriched in recent decades by its relationship with string theory. We will cover the basics of symplectic geometry, including:
- Definitions: symplectic linear algebra, symplectic manifolds, symplectomorphisms, Langrangian submanifolds.
- Local forms: Moser's theorem, Darboux' theorem, Weinstein neighbourhood theorems.
- Kaehler geometry: complex and almost complex structures, Kaehler manifolds, Dolbeault cohomology, Hodge theory,
- Moment maps: Hamiltonian mechanics, Noether's theorem, Delzant's classification of symplectic toric manifolds.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
Students MUST have passed:
Honours Complex Variables (MATH10067) AND
Honours Algebra (MATH10069) AND
Differential Geometry (MATH11235)
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | With permission of the lecturer, Algebraic Geometry can be taken simultaneously.
Note that PGT students on School of Mathematics MSc programmes are not required to have taken pre-requisite courses, but they are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling.
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Information for Visiting Students
| Pre-requisites | Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2026/27, Available to all students (SV1)
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Quota: None |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
71 )
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| Assessment (Further Info) |
Written Exam
0 %,
Coursework
100 %,
Practical Exam
0 %
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| Additional Information (Assessment) |
Coursework 100% |
| Feedback |
Not entered |
| No Exam Information |
Learning Outcomes
On completion of this course, the student will be able to:
- Learn one of the methods that have become essential for the study of Geometry and Topology during the 20th century.
- Explain the method's underlying definitions and essential constructions and provide examples illustrating them.
- Understand application of the method for fundamental results in the area and demonstrate this understanding by explaining key steps in the proof of these fundamental results.
- Apply this method as a problem-solving tool.
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Reading List
| Daniel Huybrechts, Complex Algebraic Geometry, An Introduction. |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | MMGT |
Contacts
| Course organiser | Dr John Pearson
Tel: (0131 6)50 5049
Email: J.Pearson@ed.ac.uk |
Course secretary | Mr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk |
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