Arithmetic geometry, especially arithmetic and computational aspects of curves and abelian varieties over arithmetic fields, their rational points, L-functions, and cohomology
- computational (with theoretical aspects):
- explicit methods for abelian varieties: strong Birch–Swinnerton-Dyer conjecture over number fields
funded by the DFG, see also the DFG-funded follow-up project with the proposal written by Michael Stoll and me and Pip Goodman being employed on that position and working together with us
- explicit Mordell conjecture for curves: Chabauty method (both classical and non-abelian) and its application to rational points on modular and Shimura curves
- theoretical: Birch–Swinnerton-Dyer conjecture over higher-dimensional bases in positive characteristic
You can find the code for my articles on GitHub when they are published.