I'm Timo Keller. I'm interested in (computational) arithmetic geometry.
Here is code for some articles I'm involved in on GitHub:
Birch–Swinnerton-Dyer Conjecture
- https://github.com/TimoKellerMath/strongBSDgenus2 (Complete verification of strong BSD for many modular abelian surfaces over Q https://arxiv.org/abs/2312.07307 with Michael Stoll)
Rational points on modular curves
-
https://github.com/sachihashimoto/X0Nstarquotients (Rational points on
$X_0(N)^*$ when$N$ is non-squarefree https://arxiv.org/abs/2505.00680 with Sachi Hashimoto and Samuel Le Fourn) -
https://github.com/davidlowryduda/isolated_points (Towards a Classification of Isolated
$j$ -invariants https://arxiv.org/abs/2311.07740 with Abbey Bourdon, Sachi Hashimoto, Zev Klagsbrun, David Lowry-Duda, Travis Morrison, Filip Najman, and Himanshu Shukla) -
https://github.com/TimoKellerMath/QuadraticPoints (Computing quadratic points on modular curves
$X_0(N)$ https://arxiv.org/abs/2303.12566 with Nikola Adžaga, Philippe Michaud-Jacobs, Filip Najman, Ekin Ozman, and Borna Vukorepa) -
https://github.com/shiva-chid/Hyperelliptic_X0Nstarquotients (quadratic Chabauty for hyperelliptic
$X_0(N)^*$ https://arxiv.org/abs/2203.05541 with Nikola Adžaga, Shiva Chidambaram, and Oana Padurariu) -
https://github.com/shiva-chid/ModularCurvesX0plusG4-6 (quadratic Chabauty for
$X_0(p)^+$ of genus 4, 5, and 6 https://arxiv.org/abs/2105.04811 with Nikola Adžaga, Vishal Arul, Lea Beneish, Mingjie Chen, Shiva Chidambaram, and Boya Wen)
Inverse Galois theory for 17T7
- https://github.com/SamSchiavone/17T7 and https://github.com/edgarcosta/EichlerShimuraHMF (17T7 is a Galois group over the rationals https://arxiv.org/abs/2411.07857, with Raymond van Bommel, Edgar Costa, Noam D. Elkies, Sam Schiavone, and John Voight)
Work in progress (MIT workshops https://math.mit.edu/~edgarc/MCW.html, https://math.mit.edu/~edgarc/MCW2.html and https://math.mit.edu/~edgarc/MCW3.html on the LMFDB https://www.lmfdb.org):