Arithmetic Geometry
Rational Curves and Conics
Rational curves and conics: models and rational points.
Elliptic Curves
Elliptic curve creation, arithmetic, and the function field.
Elliptic Curves over Finite Fields
Supersingular curves, point counting, group structure, and pairings.
Elliptic Curves over Q and Number Fields
Curves over number fields and p-adic fields, and Mordell-Weil groups.
Elliptic Curves over Function Fields
Curve search, heights, and torsion over function fields.
Models of Genus One Curves
Genus one curve models, transformations, and equivalence.
Plane Quartics
Quartic invariants, reconstruction from invariants, and twists.
Hyperelliptic Curves
Hyperelliptic curve models and divisor arithmetic.
Hypergeometric Motives
Hypergeometric motives and Jacobi motives.
L-Functions
Built-in and general L-series, and their invariants.