B3.2 Geometry of Surfaces (2022-23)
Topic outline
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These are Nigel Hitchin's 2013 Geometry of Surfaces lecture notes. I based my lectures on them, and they are the primary reference for the course.
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These are the handwritten slides for the pre-recorded lectures in the COVID year 2020, in one file. Divided into Lectures 1-18 and sections 1-5. They more-or-less exactly correspond to what I intend to write on the board in lectures, though divided into 18 rather than 16.
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This is an initial optional problem sheet to get you started before the classes. Do not hand in solutions. It is based on the first three lectures, sections 1-2.5 in the slides, on topological surfaces, Hitchin notes chapter 2. Sample solutions are on the course web page.
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This is the problem sheet for the first class in weeks 2 or 3. It is based on the first five lectures on topological surfaces, sections 1-2 in the slides, Hitchin notes chapter 2. Please hand in solutions.
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This is the problem sheet for the second class in weeks 4 or 5. It is based on lectures 5-8 on Riemann surfaces, section 3 in the slides, Hitchin notes chapter 3. Please hand in solutions.
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This is the problem sheet for the third class in weeks 6 or 7. It is based on lectures 9 - 14 on smooth surfaces and Riemannian metrics as far as the statement of the Gauss-Bonnet Theorem, sections 4.1-4.10 in the slides, Hitchin notes sections 4.1-4.6. Please hand in solutions.
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This is the problem sheet for the fourth class in week 8 or week 1 of HT23. It is based on lectures 13 - 16 on geodesics, critical points, and the hyperbolic plane, sections 4.9, 4.11 and 5 in the slides, Hitchin notes sections 4.6-4.7 and 5. Please hand in solutions.
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