Quaternion algebras: Computational methods and the Langlands program
Fall 2015
Course Info:
- Lectures: Monday, Wednesday, Friday: 10:00 a.m. - 11:00 a.m.)
- Dates: 14 September 2015 - 13 November 2015
- Room: ICERM Lecture Hall, 11th floor
- Instructor: John Voight
- E-mail: jvoight@gmail.com
- Office hours: Please e-mail me for an appointment
- Course Web Page: http://www.math.dartmouth.edu/~jvoight/ICERM-quat/
- Prerequisites: None.
- Required Texts: None (course notes).
This course will provide an introduction to quaternion algebras with an emphasis on computational aspects and applications to the Langlands program.
Please see the latest book draft.
| Module 1: Quaternionic basics | ||||
| 1 | 14 Sep | (M) | Introduction: basics and modular curves | |
| 2 | 16 Sep | (W) | Introduction: Brandt matrices and Shimura curves | |
| 3 | 18 Sep | (F) | Splitting and quadratic forms | |
| 4 | 21 Sep | (M) | Classification over local and global fields | |
| 5 | 23 Sep | (W) | Orders | |
| - | 25 Sep | (F) | No class, JV at Dartmouth | |
| - | 28 Sep - 2 Oct | (M-F) | No class, ICERM workshop 1 | |
| Module 2: Definite algorithms | ||||
| 6 | 5 Oct | (M) | Ideals | |
| 7 | 7 Oct | (W) | Brandt matrices | |
| - | 9 Oct | (F) | No class | |
| - | 12 Oct | (M) | No class, Columbus Day | |
| 8 | 14 Oct | (W) | Examples and generalizations | |
| 9 | 16 Oct | (F) | Algebraic modular forms | |
| - | 19 Oct - 23 Oct | (M-F) | No class, ICERM workshop 2 | |
| Module 3: Indefinite algorithms | ||||
| 10 | 26 Oct | (M) | Quaternionic arithmetic groups | |
| 11 | 28 Oct | (W) | Shimura curves over Q: discriminant 6 | |
| - | 30 Oct | (F) | No class, JV at Yale | |
| - | 2 Nov | (M) | No class | |
| 12 | 4 Nov | (W) | Shimura curves, more generally | |
| 13 | 6 Nov | (F) | Algorithms in group cohomology | |
| - | 9 Nov - 13 Nov | (M-F) | No class, ICERM workshop 3 | |