MAT 543 Fall 2019 Homepage
MAT 543 Fall 2019 Assignments and Exams
MAT 543 Syllabus
Complex Analysis II
Fall 2019
The schedule for topics covered in lecture is as follows.
Monday, August 26
Overview of Riemann surface, holomorphic line bundles, and meromorphic sections.
Wednesday, August 28
Overview of cohomology, Riemann-Roch, and Riemann-Hurwitz.
Monday, September 2
Labor Day. No class.
Wednesday, September 4
Section 1. The definition of Riemann surfaces.
Monday, September 9
Sections 2 and 3. Elementary properties of holomorphic mappings. Homotopy of Curves. The fundamental group.
Wednesday, September 11
Section 4. Branched and unbranched coverings.
Monday, September 16
Section 5. The universal covering and covering transformations.
Wednesday, September 18
Sections 6 and 7. Sheaves. Analytic continuation.
Problem Set 1
due in lecture.
Monday, September 23
Section 8. Algebraic functions.
Wednesday, September 25
Section 9. Differential forms.
Problem Set 2
due in lecture.
Monday, September 30
Section 10. The integration of differential forms.
Wednesday, October 2
Section 12. Cohomology groups.
Problem Set 3
due in lecture.
Monday, October 7
Section 13. Dolbeault's lemma.
Wednesday, October 9
Section 14. A finiteness theorem.
Problem Set 4
due in lecture.
Monday, October 14
Fall break. No class.
Wednesday, October 16
Section 15. The exact cohomology sequence.
Problem Set 5
due in lecture.
Monday, October 21
Section 16. The Riemann-Roch theorem.
Wednesday, October 23
Section 17. The Serre duality theorem.
Problem Set 6
due in lecture.
Monday, October 28
Section 18. Functions and differential forms with prescribed principal parts.
Wednesday, October 30
Section 19. Harmonic differential forms.
Problem Set 7
due in lecture.
Monday, November 4
Section 20. Abel's theorem.
Wednesday, November 6
Section 21. The Jacobi inversion problem.
Problem Set 8
due in lecture.
Monday, November 11
Section 22. The Dirichlet boundary value problem.
Wednesday, November 13
Section 24. Weyl's Lemma.
Problem Set 9
due in lecture.
Monday, November 18
Section 25. The Runge approximation theorem.
Wednesday, November 20
Section 26. The theorems of Mittag-Leffler and Weierstrass.
Problem Set 10
due in lecture.
Monday, November 25
Section 27. The Riemann mapping theorem.
Deadline to confirm oral presentation topic with instructor.
Wednesday, November 27
Thanksgiving. No class.
Monday, December 2
Section 29. Line and vector bundles.
Wednesday, December 4
Sections 30 and 31. The triviality of vector bundles. The Riemann-Hilbert problem.
Monday, December 9
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