Arithmetic geometry, especially arithmetic and computational aspects of curves and abelian varieties over arithmetic fields, their rational points, L-functions, and cohomology
- abelian varieties and the Birch–Swinnerton-Dyer conjecture:
- over number fields: explicit methods and Iwasawa theory
- in positive characteristic: over higher-dimensional bases
- rational points on (modular) curves: explicit and theoretical methods, for example using the Chabauty–Kim method
You can find the code for my articles on GitHub when they are published.