Math 583e -- Computational Number Theory (part 2)

MWF at 1:30pm in MEB 243
Course Notes for Modular Abelian Varieties part of the course: modabvar.pdf
Professors: William Stein and Bill Hart
Topics:
1. Integer factorization
2. Modular abelian varieties
Google group mailing list: http://groups.google.com/group/583-uw09
Schedule
Grading: Your grade will be based entirely on 2 projects, one on integer factorization (due April 27), and one on modular abelian varieties (due June 5). There will be no graded homework.
Projects
References:
- My 2003 Harvard course on modular abelian varieties (Stein)
- Rough notes in progress for this part of the course [linked pdf] (Stein)
- Algorithms for Modular Elliptic Curves (Cremona)
- Studying the Birch and Swinnerton-Dyer Conjecture for Modular Abelian Varieties Using MAGMA (Stein)
- An introduction to computing modular forms using modular symbols (Stein)
- Modular Forms, A Computational Approach (Stein)
- The Manin Constant (Agashe, Ribet, Stein)
- Visible Evidence for the Birch and Swinnerton-Dyer Conjecture for Rank 0 Modular Abelian Varieties (Agashe-Stein)
- Visibility of Shafarevich-Tate Groups of Abelian Varieties (Agashe-Stein)
- Component Groups of Purely Toric Quotients of Semistable Jacobians (Conrad-Stein)
- Explicit approaches to modular abelian varieties (Stein)
- Osserman's MIT student reading seminar from 2001 on Kolyvagin's Euler System