Workshop on Algorithms in Number Theory and Arithmetic Geometry

Leiden, 31 July–4 August 2017

Projects

(Nils, Jeroen) SageMath 8.0 has now sage.schemes.riemann_surfaces.riemann_surface.RiemannSurface for numerical computation of period matrices. Integrate this code better into the rest of sage, e.g.:
- put a method on plane algebraic curves to get the corresponding Riemann surface?
- Improve the Gauss-Legendre integrator to compute the integration nodes in a more efficient way?
- There is already code to compute a Z-basis for the endomorphism ring numerically. Perhaps support computations of isogenies as well? (Jeroen)
- Make the Rosati involution available? (Jeroen)

Mordell-Weil groups of Elliptic curves over function fields (Bartosz, Peter)
Bounding gonalities of curves
Finite fields:
Add a wrapper for flint fq implementation into sage (ticket #16664, more up to date version in ffisom repo)
Add an fp type to flint (basic implem in ellmul)
clean up and package ffisom
$p$ -adic fields:
finish tickets from sage days 87
Cryptography based on supersingular elliptic curves (supersingular isogeny key exchange) (Bas, Marco), use Luca's code ? A student of his is also working on using ordinary cuves in Julia/Nemo.
L-function computations for elliptic curves over number fields (Maarten)
Access new PARI functionality from SageMath (Peter, Vincent, Marc)
- cypari2 Pull Request 28: autogeneration of Cython headers
- cypari2 Issue 29: run tests with various PARI/GP versions
- Use latest development version of PARI: see https://wiki.sagemath.org/PariDevInSage
Generate modular forms using products of Eisenstein series (Henri, Kamal)
Packaging Sage code outside the Sage distribution (Marc)
Review open SageMath tickets (https://trac.sagemath.org/)
Update the SageMath version of Denis Simon's GP scripts (http://www.math.unicaen.fr/~simon/) to the latest version

Maarten Derickx - $A$ -gonalities of curves and the existence of inifinitely many points of degree $d$ . Slides