Elliptic Curves and Modular Forms
Chuck Doran (University of Alberta)Sep 3, 2025 — Dec 3, 2025
About the course
This course is an introduction to the theory of elliptic curves and modular forms at the graduate level. Elliptic curves will be introduced through both their classical analytic construction over the real and complex numbers and their algebraic realizations via normal forms over arbitrary fields. Moduli and monodromy considerations lead us to study the special role of the elliptic modular group SL(2,Z) and the crucial notions of modular functions and forms. Studying torsion points and level structure then motivates the extension to finite index subgroups and the theory of modular curves. Throughout the course, there will be an emphasis on hands-on explicit computations. Directed by the instructor, each student will complete a final project, presentation, and paper. Possible topics could include post-quantum elliptic curve cryptography, applications in string theory, geometry of elliptic modular surfaces, features of periods and Picard-Fuchs operators, etc.
Registration
This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.
Enrollment Details
- Course Name
- Elliptic Curves and Modular Forms
- Date
- Sep 3, 2025 — Dec 3, 2025
- Course Number
- Section Number
- Section Code
Instructor(s)
For help with completing the Western Dean’s agreement form, please contact the graduate student program coordinator at your institution. For more information about the agreement, please see the Western Dean's Agreement website
Other Course Details
Class Schedule
- TBA
Remote Access
The course will be taught over Zoom using a tablet and shared screen. Lecture notes will be written out live on a tablet. There will also be pre-prepared slides on certain topics. The in-class lecture notes will be saved and distributed as .pdf files. There will be a course webpage to host all of these plus additional course materials and readings.
The format will be Zoom based, with videos on. Breakout rooms will be used periodically for small group work. Students will be encouraged to “raise hands” with questions at any time.
Availability
This course may be open to students from universities outside of the PIMS network, and those coming from industry/government.