MAT 401 Fall 2019 Course Information

401 Course Policy

Homework Assignments:

Homework 1

Homework 2

Homework 3

Homework 4

Homework 5

Homework 6

Announcements/Schedule:

Tentative Presentation Schedule
Tue 8/271. Introduction, Riemann Surface definition and examples.
Thu 8/292. More examples. Morphisms
Tue 9/33. Morphisms, examples. Holomorphic differentials
Thu 9/5 4. Holomorphic differentials
Tue 9/105. Topology of Riemann surfaces Marc Julien Calza (26-30) and Liuming Wang (30-35)
Thu 9/126. Fundamental Group Connor Stewart (36-39) and Yuhao Liu (39-Residue Thm)
Tue 9/177. Coverings Albert Guo (47-52) and Pablo Mingwang Zhou Wang (53-56)
Thu 9/198. Coverings Julian Michele (57-60) and Kunhui Luan (61-63)
Tue 9/249. Curves, function fields, and Riemann surfaces Rentai Hou (69-71)
Thu 9/2610. Function field of a Riemann surface
Tue 10/111. No class. Time to be re-scheduled.
Thu 10/612. Function field of a Riemann surface
Tue 10/813. Belyi's Theorem--Introduction
Thu 10/1014. Belyi's Theorem--Proof in one direction
Tue 10/15 Fall Break, No Class
Thu 10/1715 Galois Theory Marc Julien Calza
Tue 10/2216. No class. Time to be rescheduled.
Thu 10/2417 Belyi's Theorem Lisa Berger
Tue 10/2918 Belyi's Theorem Connor Stewart (183-185) and Lisa Berger (185-188)
Tue 10/3119 Belyi's Theorem Albert Guo and Lisa Berger (188-191) and (191-193)
Tue 11/520 Belyi's Theorem Julian Michele and Liuming Wang (193-198)
Thu 11/721 Belyi's Theorem Yuhao Liu (198-201) and Pablo Mingwang Zhou Wang (201-204)
Tue 11/1222 Dessins Lisa Berger and Kunhui Luan
Thu 11/1423 Dessins
Tue 11/1924 Dessins
Thu 11/2125 Dessins
Tue 11/2626 Dessins
Thu 11/28 Thanksgiving Break, No Class
Tue 12/327 Dessins
Tue 12/528 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