- p-adic numbers;
- valuations (by Julian Rüth);
- semistable models of curves.
- isomorphisms, invariants and reconstruction for hyperelliptic curves (with Reynald Lercier and Christophe Ritzenthaler);
- isomorphisms, invariants and reconstruction for plane quartic curves (with Reynald Lercier and Christophe Ritzenthaler);
- calculating endomorphism rings of Jacobians (with Edgar Costa, Nicolas Mascot, and John Voight);
- canonical models of arithmetic (1; inf)-curves;
- gluing of Jacobians of curves of genus 1 and 2 (with Jeroen Hanselman);
- functionality for CM curves (with Bogdan Dina and Sorina Ionica).