CMI Workshop: Computational Arithmetic Geometry
September 30 – October 3, 2007
The goal of this workshop is to study explicit computation with Monsky-Washnitzer cohomology, Coleman integration, Iwasawa theory, the Birch and Swinnerton-Dyer conjecture, Stark-Heegner points, and modular forms. We also intend to create and discuss practical implementations in the open source computer software SAGE of many of the associated algorithms.
The workshop will discuss
- new techniques and algorithms for explicit computation in arithmetic geometry;
- research areas and open problems that may benefit from these techniques and algorithms;
- improvement of freely available general purpose software for research in arithmetic geometry.
Schedule
| 9:15-10:15 | William Stein, On Convergence in the Sato-Tate Conjecture |
| 10:30-11:30 | David Roe, p-adic Arithmetic in SAGE |
| 1:00-2:00 | Fernando Rodriguez-Villegas, Identities between p-adic Multi-Polylogs and p-adic Zeta Values |
| 2:30-3:30 | William Stein, Overall Sage Status Report and Project Organizational Meeting |
| 7:00-7:30 | William Stein and/or Robert Bradshaw, Algebraic Number Theory in SAGE, a Status Report |
| 7:30-8:00 | Craig Citro, Modular Forms in SAGE, a Status Report |
| 8:00-? | Evening Working Session |
Monday, October 1
| 9:15-10:15 | Amnon Besser, On the Computation of p-adic Height Pairings on Jacobians of Hyperelliptic Curves |
| 10:30-11:30 | Robert Bradshaw & Kiran Kedlaya, Coleman Integration |
| 1:00-2:00 | Martin Albrecht, Commutative Algebra and Sparse Linear Algebra in SAGE (Singular, PolyBoRi) |
| 7:00-7:30 | Bill Hart, On Short Division: FLINT (Fast Library for Number Theory), a Status Report |
| 7:30-8:00 | Michael Abshoff, Managing the SAGE Development Workflow |
| 8:00-? | Evening Working Session |
Tuesday, October 2
| 9:15-10:15 | Gonzalo Tornaria, Stark-Heegner Points and the Shimura Correspondence |
| 10:30-11:30 | Dimitar Jetchev, Computing Higher Heegner Points and Verifying a Conjecture of Kolyvagin |
| 1:00-2:00 | Michael Abshoff, [Ap]CoCoALib |
| 7:00-7:30 | Robert Bradshaw, Cython Status Report |
| 7:30-8:00 | Robert Bradshaw, Coercion Status Report |
| 8:00-? | Evening Working Session |
Wednesday, October 3
| 9:00-10:00 | J-P. Serre, Finite Groups in Number Theory (part 3)
At Science Center 507, Harvard |
| 11:00-12:00 | William Stein, Computing p-adic Invariants of Elliptic Curves and Applications of Iwasawa Theory to BSD |
| 1:00-2:00 | Wrap Up |
| 3:00-4:00 | Mark Watkins, Ranks of Elliptic Curves
At Science Center 507, Harvard |
| 8:00-? | Evening Working Session |
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