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