Non-abelian Chabauty and rational points on curves.
Progress on Mazur's Program B.
A-gonality and points of degree d on curves.
Torsion Points and Isogenies on CM Elliptic Curves.
Elliptic Curves of Prime Conductor.
Modular symbols for Fermat Curves.
An $\ell-p$ switch trick to obtain a new proof of a criterion for arithmetic equivalence.
Upper bounds for the endomorphism algebra of an abelian variety.
Shioda's fourfold and CM Mumford's fourfold.
Odd order obstructions to rational points on general K3 surfaces.
Computing hyperelliptic modular invariants from period matrices.
Galois actions associated to hyperelliptic curves over local fields.
Conductors and minimal discriminants of hyperelliptic curves in odd residue characteristic.
Computing Zeta Functions of Superelliptic Curves in Large Characteristic.
Torsion Subgroups of Elliptic Curves over Function Fields.
The geometric average size of Selmer groups over function fields.
The Sato-Tate conjecture and Nagao's conjecture.