Algebraic curves defined over finite fields have long been a rich source of enquiry, bridging abstract algebra, geometry and number theory. Their automorphism groups, which consist of self-symmetries ...

Arithmetic geometry of curves stands at the crossroads of algebraic geometry and number theory, offering a rigorous framework for analysing algebraic curves defined over number and finite fields. This ...

Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others. You’re sitting at the end of a long conference table, ...

Low-dimensional topology, hyperbolic geometry and 3-manifolds, knot theory, contact geometry, curve complex and mapping class group. Low-dimensional topology, hyperbolic geometry and 3-manifolds, knot ...

Many complicated advances in research mathematics are spurred by a desire to understand some of the simplest questions about numbers. How are prime numbers distributed in the integers? Are there ...