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 joint with Michael Stoll)
Rational points on modular curves
- https://github.com/davidlowryduda/isolated_points (Towards a Classification of Isolated j-invariants https://arxiv.org/abs/2311.07740)
- https://github.com/TimoKellerMath/QuadraticPoints (Computing quadratic points on modular curves X_0(N) https://arxiv.org/abs/2303.12566)
- https://github.com/shiva-chid/Hyperelliptic_X0Nstarquotients (quadratic Chabauty for hyperelliptic X_0(N)^* https://arxiv.org/abs/2203.05541)
- 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)
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, joint 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):