Homework Assignments:
Announcements/Schedule:
Tentative Presentation Schedule
Tue 8/27 1. Introduction, Riemann Surface definition and examples. Thu 8/29 2. More examples. Morphisms Tue 9/3 3. Morphisms, examples. Holomorphic differentials Thu 9/5 4. Holomorphic differentials Tue 9/10 5. Topology of Riemann surfaces Marc Julien Calza (26-30) and Liuming Wang (30-35) Thu 9/12 6. Fundamental Group Connor Stewart (36-39) and Yuhao Liu (39-Residue Thm) Tue 9/17 7. Coverings Albert Guo (47-52) and Pablo Mingwang Zhou Wang (53-56) Thu 9/19 8. Coverings Julian Michele (57-60) and Kunhui Luan (61-63) Tue 9/24 9. Curves, function fields, and Riemann surfaces Rentai Hou (69-71) Thu 9/26 10. Function field of a Riemann surface Tue 10/1 11. No class. Time to be re-scheduled. Thu 10/6 12. Function field of a Riemann surface Tue 10/8 13. Belyi's Theorem--Introduction Thu 10/10 14. Belyi's Theorem--Proof in one direction Tue 10/15 Fall Break, No Class Thu 10/17 15 Galois Theory Marc Julien Calza Tue 10/22 16. No class. Time to be rescheduled. Thu 10/24 17 Belyi's Theorem Lisa Berger Tue 10/29 18 Belyi's Theorem Connor Stewart (183-185) and Lisa Berger (185-188) Tue 10/31 19 Belyi's Theorem Albert Guo and Lisa Berger (188-191) and (191-193) Tue 11/5 20 Belyi's Theorem Julian Michele and Liuming Wang (193-198) Thu 11/7 21 Belyi's Theorem Yuhao Liu (198-201) and Pablo Mingwang Zhou Wang (201-204) Tue 11/12 22 Dessins Lisa Berger and Kunhui Luan Thu 11/14 23 Dessins Tue 11/19 24 Dessins Thu 11/21 25 Dessins Tue 11/26 26 Dessins Thu 11/28 Thanksgiving Break, No Class Tue 12/3 27 Dessins Tue 12/5 28 Dessins Tue 12/19 Student Presentations 11:15 -- 1:45
Some Books and Articles:
For Riemann Surfaces:Miranda, Rick Algebraic curves and Riemann Surfaces
Jost, Jürgen Compact Riemann Surfaces
Jones, G., and Singerman, D., Complex functions: An algebraic and geometric viewpoint
For Covering maps and fundamental group:
Hatcher, Alan Algebraic Topology
On Belyi functions and Dessins:
Jones, G., and Singerman, D., Belyi functions, hypermaps and Galois groups Bulletin of the London Mathematical Society, 28 (1996), 561-590