Arithmetic Geometry

Rational Curves and Conics

Rational curves and conics: models and rational points.

Rational Curves and Conics

Elliptic Curves

Elliptic curve creation, arithmetic and the function field.

Elliptic Curves

Elliptic Curves over Finite Fields

Supersingular curves, point counting, group structure and pairings.

Elliptic Curves over Finite Fields

Elliptic Curves over Q and Number Fields

Curves over number fields and p-adic fields, and Mordell-Weil groups.

Elliptic Curves over {\mathbb{Q}} and Number Fields

Elliptic Curves over Function Fields

Curve search, heights and torsion over function fields.

Elliptic Curves over Function Fields

Models of Genus One Curves

Genus one curve models, transformations and equivalence.

Models of Genus One Curves

Plane Quartics

Quartic invariants, reconstruction from invariants, and twists.

Plane Quartics

Hyperelliptic Curves

Hyperelliptic curve models and divisor arithmetic.

Hyperelliptic Curves

Hypergeometric Motives

Hypergeometric motives and Jacobi motives.

Hypergeometric Motives

L-Functions

Built-in and general L-series, and their invariants.

L-Functions