Geometry III / Introduction to Geometry III

The purpose of this course is to gives an introduction to the Riemann surfaces, following the lectures notes by Dustin Clausen available at this link. My own notes from Lectures 1-11 are available below.

Time and place: Thursday 2:45-4:15 in Science Building 1, Room 509.

Lecture notes:

Lecture 1: Review of holomorphic functions
Lecture 2: Algebraic functions and analytic continuation
Lecture 3: Structured surfaces
Lecture 4: The implicit function theorem
Lecture 5: Statement of the main theorems
Lecture 6: Local structure of holomorphic maps
Lecture 7: The Riemann sphere
Lecture 8: Riemannian geometry
Lecture 9: The Iwasawa decomposition
Lecture 10: Elliptic curves from lattices
Lecture 11: The universal cover

Problem sets:

Problem set 1.
Problem set 2.
Problem set 3.
Problem set 4.
Problem set 5.