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