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MA475 Riemann Surfaces

Example Sheets for 2020:

Example Sheet 1

Example Sheet 2

Example Sheet 3

Example Sheet 4

Example Sheet 5

Lecture notes from 2020:

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Lecture 6

Lecture 7

Lecture 8

Lecture 9

Lecture 10

Lecture 11

Lecture 12

Lecture 13

Lecture 14

Lecture 15

Lecture 16

Lecture 17

Lecture 18

Lecture 19

Lecture 20

Lecture 21

Lecture 22

Lecture 23

Lecture 24

Lecture 25

Lecture 26

Lecture 27

Lecture 28

Lecture 29

Lecture 30

Older material is listed below.

Lecture notes for 2019:

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Lecture 6

Lecture 7

Lecture 8

Lecture 9 The sphere, Group actions

Lecture 10 The torus. Main theorem statement

Lecture 11 Surfaces in C^2

Lecture 12 Hyper-elliptic surfaces

Lecture 13 More hyper-elliptic discussion

Lecture 14 Meromorphic functions, isolated singularities

Lecture 15 Meromorphic functions on S^2

Lecture 16 Local form for holomorphic functions

Lecture 17 Holomorphic 1 forms

Lecture 18 Holomorphic 1 forms on C^2

Lecture 19 Schwartz's Lemma

Lecture 20 Schwartz-Pick

Lecture 21 The degree theorem

Lecture 22 Riemann-Hurwitz

Lecture 23 Functions on T^2

Lecture 24 Weierstrass function

Lecture 25 Polynomial equation

Lecture 26 Conformal isomorphism

Lecture 27 Integration and periods

Lecture 28 Space of lattices

Lecture 29 Functions on moduli space

Lecture 30 Geometry of 1-forms

Example sheets for 2019:

Example Sheet 1

Example Sheet 2

Example Sheet 3

Example Sheet 4

Example Sheet 5

Course contents for 2018:

Topic outline

Definition of Riemann surfaces (Uploaded 13 April)

Implicit function theorem (Uploaded 16 April)

Affine and projective varieties (Uploaded May 14)

Local structure of holomorphic maps and structure of proper holomorphic maps (Uploaded 16 April)

Meromorphic functions on CP1 (Uploaded 15 April)

2018 Covering space notes (Updated 11 April)

2018 Weierstrass P functions and Riemann-Hurwitz (Updated 15 April)

Lecture notes from 2017:

Covering space discussion

Riemann surfaces and atlases

Notes 1

Notes 2

Notes 3

Notes 4

Algebraic curves and holomorphic maps

Notes 5

Notes 6

Notes 7

Notes 8

Notes 9

Topology and holomorphic maps

Notes 10

Notes 11

Notes 12

Notes 13

Notes 14

Notes 15

The Weierstrass P function

Notes 16

Notes 17

Notes 18

Notes 19

Notes 19.5

The uniformisation theorem and conclusion

Notes 20

Notes 21

Notes 22

Notes 23