Quaternion algebras: Computational methods and the Langlands program

Fall 2015

 

Course Info:

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
114 Sep(M)Introduction: basics and modular curves
216 Sep(W)Introduction: Brandt matrices and Shimura curves
318 Sep(F)Splitting and quadratic forms
421 Sep(M)Classification over local and global fields
523 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
65 Oct(M)Ideals
77 Oct(W)Brandt matrices
-9 Oct(F)No class
-12 Oct(M)No class, Columbus Day
814 Oct(W)Examples and generalizations
916 Oct(F)Algebraic modular forms
-19 Oct - 23 Oct(M-F)No class, ICERM workshop 2
Module 3: Indefinite algorithms
1026 Oct(M)Quaternionic arithmetic groups
1128 Oct(W)Shimura curves over Q: discriminant 6
-30 Oct(F)No class, JV at Yale
-2 Nov(M)No class
124 Nov(W)Shimura curves, more generally
136 Nov(F)Algorithms in group cohomology
-9 Nov - 13 Nov(M-F)No class, ICERM workshop 3