MAT 543 Course Webpage Complex Analysis II Mon Wed 12 PM — 1:20PM, Math Tower 4 —130 Fall 2019

Course Announcements Announcements about the course will be posted here. Please check the site regularly for announcements (which will also be given in lecture).

• To see how some of the language of simplicial objects can be used to set-up and study Čech cohomology, please take a look at Problem Sets 8 and 9 here. In particular, Problem 5(c). p. 18 on Problem Set 8 explains the simplicial homotopy that extends the proof of Lemma 12.3, p. 98, to higher Čech cohomology.

Course Description The description in the graduate bulletin: "Monodromy theorem and analytic continuation. Elliptic functions. Dirichlet problem and Green's function. Conformal mappings. Introduction to Riemann surfaces and, or several complex variables."
There will be an emphasis on concepts that are ubiquitous in geometry: the use of sheaves, interpretation via manifolds, and use of harmonic theory. After this course, each student should be well-prepared to pursue complex geometry as in Griffiths-Harris or Wells.

Prerequisites This course is intended as a successor to MAT 536. Students who have not passed MAT 536 (or had this course waived by the Graduate Director) should speak with the instructor as soon as possible.

Text There is no required textbook. The lectures and assignments will be drawn from the recommended textbook, Lectures on Riemann surfaces by Otto Forster, translated by Bruce Gilligan. There are many other excellent textbooks on this topic. Students may use whatever textbook they prefer, but it will be useful to refer to Forster's book.

Lectures The instructor for this course is Jason Starr.

Lecture is held Mondays and Wednesday, 12 NOON — 1:20 PM in Math Tower 4—130.

Office Hours

• Monday 10AM — 11AM, Math Tower P—143 (advising).
• Monday 1:25PM — 2:25PM, Math Tower 4—108.
• Wednesday 10AM — 11AM, Math Tower 4—108.

Grading System Grading will be based on completed assignments, class participation, and a final oral report by each student. All undergraduate students and all graduate students who have not yet passed the comprehensive exam should contact the instructor as soon as possible.

Required Syllabi Statements
The University Senate Undergraduate and Graduate Councils have authorized that the following required statements appear in all teaching syllabi (graduate and undergraduate courses) on the Stony Brook Campus.

Americans with Disabilities Act.
If you have a physical, psychological, medical or learning disability that may impact your course work, please contact the Student Accessibility Support Center, ECC (Educational Communications Center) Building, Room 128, (631)632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential.

Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and the Student Accessibility Support Center. For procedures and information go to the following website: https://ehs.stonybrook.edu/programs/fire-safety/emergency-evacuation/evacuation-guide-people-physical-disabilities and search Fire Safety and Evacuation and Disabilities.

Academic Integrity Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at https://www.stonybrook.edu/commcms/academic_integrity/index.html .

Critical Incident Management Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of University Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures.

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