Notes will be posted here in the afternoons following the lecture.
Lecture Notes |
Date |
Topic |
|
|---|---|---|---|
| #1 | | Wednesday, | Jan. 22 Conformal maps, harmonic functions | |
| #2 | | Friday, | Jan. 24 Converses to Wednesday's results | |
| #3 | | Wednesday, | Jan. 29 Riemann Mapping Thm, part I | |
| #4 | | Friday, | Jan. 31 Riemann Mapping Thm, part II: normal families | |
| #5 | | Monday, | Feb. 3 Arzela-Ascoli theorem | |
| #6 | | Wednesday, | Feb. 5 End of the Riemann Mapping Theorem pf | |
| #7 | | Friday, | Feb. 7 Linear fractional transformations | |
| #8 | | Monday, | Feb. 10 Schwarz-Christoffel transformations | |
| #9 | | Wednesday, | Feb. 12 Dirichlet problem on a disk | |
| #10 | | Friday, | Feb. 14 Using Poisson's integral | |
| #11 | | Monday, | Feb. 17 Intro to elliptic functions | |
| #12 | | Wednesday, | Feb. 19 The Weierstrass p function | |
| #13 | | Friday, | Feb. 21 Elliptic functions and elliptic curves | |
| #14 | | Monday, | Feb. 24 Intro to Riemann Surfaces | |
| #15 | | Wednesday, | Feb. 26 Examples of Riemann surfaces | |
| #16 | | Friday, | Feb. 28 More examples of Riemann surfaces | |
| #17 | | Monday, | Mar. 3 Holomorphic functions on Riemann surfaces | |
| #18 | | Wednesday, | Mar. 5 Meromorphic functions on Riemann surfaces | |
| #19 | | Friday, | Mar. 7 Nullstellensatz | |
| #20 | | Monday, | Mar. 10 End of examples of meromorphic functions | |
| #21 | | Wednesday, | Mar. 12 Holomorphic maps between Riemann surfaces | |
| #22 | | Friday, | Mar. 14 Multiplicity | |
| #23 | | Monday, | Mar. 24 Multiplicity | |
| #24 | | Wednesday, | Mar. 26 Genus and Euler characteristic of 2-manifolds | |
| #25 | | Friday, | Mar. 28 Proof of Hurwitz formula | |
| #26 | | Monday, | Mar. 31 Hyperelliptic curves | |
| #27 | | Wednesday, | April 2 Meromorphic functions on hyperelliptic curves | |
| #28 | | Friday, | April 4 Universal covers, tori | |
| #29 | | Monday, | April 7 Monodromy representation | |
| #30 | | Wednesday, | April 9 More on monodromy | |
| #31 | | Friday, | April 11 From monodromy to holomorphic maps | |
| #32 | | Wednesday, | April 16 Compactifying singular curves | |
| #33 | | Friday, | April 18 Compactifying singular curves II | |
| #34 | | Monday, | April 21 Differential forms on smooth manifolds | |
| #35 | | Wednesday, | April 23 Differential 2-forms | |
| #36 | | Monday, | April 28 de Rham cohomology | |
| #37 | | Wednesday, | April 30 Cohomology of surfaces | |
| #38 | | Friday, | May 2 Complex structure on real forms | |
| #39 | | Monday, | May 5 Dolbeault cohomology and the "main theorem" | |
| #40 | | Wednesday, | May 7 Statement of Riemann-Roch theorem | |
| #41 | | Friday, | May 9 Proof of Riemann-Roch theorem | |
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