B3.2 Geometry of Surfaces (202223)
Topic outline


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.

These are the handwritten slides for the prerecorded lectures in the COVID year 2020, in one file. Divided into Lectures 118 and sections 15. They moreorless exactly correspond to what I intend to write on the board in lectures, though divided into 18 rather than 16.

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 12.5 in the slides, on topological surfaces, Hitchin notes chapter 2. Sample solutions are on the course web page.

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 12 in the slides, Hitchin notes chapter 2. Please hand in solutions.

This is the problem sheet for the second class in weeks 4 or 5. It is based on lectures 58 on Riemann surfaces, section 3 in the slides, Hitchin notes chapter 3. Please hand in solutions.

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 GaussBonnet Theorem, sections 4.14.10 in the slides, Hitchin notes sections 4.14.6. Please hand in solutions.

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 4.64.7 and 5. Please hand in solutions.
