SYLLABUS MATH 690G in Spring 2006
Topics in Algebra and Number Theory
1. Representation of finite and compact groups.
2. Quadratic forms, Lattices, and sphere packing problem.
3. Knots, links, and invariance.
4. Hypergeometric differential equations and hypergeometric series.
5. Classical problems: partition functions, congruence number problems, etc.
Tentative Course schedule
Week 1-4: Representation theory
Week 5-6: Hypergeometric differential equations and hypergeometric series
Week 7-8: Modular group and its subgroups
Week 9-12: Zeta functions and L-functions