MAT 543 — Fall 2017 Homepage
MAT 543 — Fall 2017 Assignments and Exams
MAT 543 Syllabus
Complex Analysis II
Fall 2017
The schedule for topics covered in lecture is as follows.
Tuesday, August 29
Overview of Riemann surface, holomorphic line bundles, and meromorphic sections.
Thursday, August 31
Overview of cohomology, Riemann-Roch, and Riemann-Hurwitz.
Tuesday, September 5
Labor Day. No class.
Thursday, September 7
Section 1. The definition of Riemann surfaces.
Tuesday, September 12
Sections 2 and 3. Elementary properties of holomorphic mappings. Homotopy of Curves. The fundamental group.
Thursday, September 14
Section 4. Branched and unbranched coverings.
Tuesday, September 19
Section 5. The universal covering and covering transformations.
Thursday, September 21
Sections 6 and 7. Sheaves. Analytic continuation.
Problem Set 1
due in lecture.
Tuesday, September 26
Section 8. Algebraic functions.
Thursday, September 28
Section 9. Differential forms.
Problem Set 2
due in lecture.
Tuesday, October 3
Section 10. The integration of differential forms.
Thursday, October 5
Section 12. Cohomology groups.
Problem Set 3
due in lecture.
Tuesday, October 10
Section 13. Dolbeault's lemma.
Thursday, October 12
Section 14. A finiteness theorem.
Problem Set 4
due in lecture.
Tuesday, October 17
Section 15. The exact cohomology sequence.
Thursday, October 19
Section 16. The Riemann-Roch theorem.
Problem Set 5
due in lecture.
Tuesday, October 24
Section 17. The Serre duality theorem.
Thursday, October 26
Section 18. Functions and differential forms with prescribed principal parts.
Problem Set 6
due in lecture.
Tuesday, October 31
Section 19. Harmonic differential forms.
Thursday, November 2
Section 20. Abel's theorem.
Problem Set 7
due in lecture.
Tuesday, November 7
Section 21. The Jacobi inversion problem.
Thursday, November 9
Section 22. The Dirichlet boundary value problem.
Problem Set 8
due in lecture.
Tuesday, November 14
Section 24. Weyl's Lemma.
Thursday, November 16
Section 25. The Runge approximation theorem.
Problem Set 9
due in lecture.
Tuesday, November 21
Section 26. The theorems of Mittag-Leffler and Weierstrass.
Deadline to confirm oral presentation topic with instructor.
Thursday, November 23
Thanksgiving. No class.
Tuesday, November 28
Section 27. The Riemann mapping theorem.
Thursday, November 30
Section 29. Line and vector bundles.
Problem Set 10
due in lecture.
Tuesday, December 5
Sections 30 and 31. The triviality of vector bundles. The Riemann-Hilbert problem.
Thursday, December 7
Additional topics.
Back to my home page.
Jason Starr
4-108 Math Tower
Department of Mathematics
Stony Brook University
Stony Brook, NY 11794-3651
Phone: 631-632-8270
Fax: 631-632-7631
Jason Starr