| Contact Information |
Lecturer : Stefan Lemurell, Room MV:L3034, Tel.: (031) 7725303, sj@chalmers.se
| Schedule |
The course will meet 15 times for 2 x 45 minutes. Initially once a week and later twice a week.
The time for the first 3 lectures will be Thursdays (28/2, 7/3, 14/3) 15:15-17 in MVL15.
| Literature |
The course will approximately follow the first 5 chapters of "A First Course in Modular Forms" by Fred Diamond and Jerry Shurman. The book is available from Chalmers library as an e-book.
Other highly recommended books for different points of view:
| Program and Examination |
The teaching will involve lectures , according to the schedule above. Examination will be by means of 5 written homeworks, plus an oral exam in May/June. To pass the course, one will need to pass the oral exam and attain at least 50% overall. In computing the final grade, 50% will be given to the homeworks and 50% to the exam performance.
Grade thresholds will be computed according to the following schemes :
Chalmers
undergraduates: < 50% (U), 50-66% (3), 67-80% (4),
81-100% (5).
GU
undergraduates: < 50% (U), 50-80% (G), 81-100% (VG).
PhD
students at MV: To pass the course, you must attain the
equivalent of a Chalmers 4-grade. i.e.: at least 67%.
PhD
students from other departments: Your grade will be
computed as for Chalmers undergraduates, at which point it is up to
your examiner to determine whether to award you pass or fail.
NOTE: Students are allowed to collaborate on homeworks, but each person must write and hand in their own solutions and indicate with whom they have collaborated.
| Week-by-week Schedule |
As we proceed, completed material will be marked in green.
OBS! The following schedule is approximate and will be continuously updated.
| Week | Date | Time | Location | Stuff |
| 9 | 28/2 | 15-17 | MVL15 | Modular group, definition and first examples of modular forms |
| 10 | 7/3 | 15-17 | MVL15 | Cancelled |
| 11 | 14/3 | 15-17 | MVL15 | Congruence subgroups |
| 12 | 20/3 | 15-17 | MVL15 | Complex tori and Elliptic curves, Modular curves and Moduli spaces |
| 13 | 27/3 | 15-17 | MVL15 | Modular curves as Riemann surfaces |
| 14 | 3/4 | 15-17 | MVL15 | Cusps, Dimension formulas |
| 16 | 16/4 | 10-12 | MVL15 | Dimension formulas (genus, automorphic forms) |
| 18/4 | 15-17 | MVL15 | Dimension formulas (meromorphic differentials) | |
| 17 | 23/4 | 10-12 | MVL15 | Dimension formulas (divisors, Riemann Roch) |
| 25/4 | 15-17 | MVL15 | Dimension formulas (even weight) | |
| 18 | 30/4 | 10-12 | MVL15 | Eisensteins series |
| 2/5 | 15-17 | MVL15 | Eisensteins series | |
| 19 | 7/5 | 10-12 | MVL15 | Hecke operators |
| 8/5 | 15-17 | MVL15 | Hecke operators | |
| 20 | 14/5 | 10-12 | MVL15 | Hecke operators |
| 16/5 | 15-17 | MVL15 | Hecke operators | |
| 21 | 22/5 | 15-17 | Summing up | |
| 21-23 | Oral exam, choose a time that suits you |
| Homeworks |