## Algebraic Number Theory and Arithmetic Algebraic Geometry

The research interests of this group are in the fields of algebraic number theory, arithmetic geometry and in the application of the above topics in experimental number theory, computational algebra and algebraic coding theory. Questions studied involve the arithmetic and geometry of curves over p-adic and finite fields, their automorphism groups and Galois covers, function field arithmetic and Drinfeld modules.

The group has three faculty members: Prof Florian Breuer, Dr Arnold Keet and Prof Barry Green who coordinate the activities and supervision of graduate students, typically 6 MSc students and 4 PhD students. There are Agreements of Cooperation with Proff Gerhard Frey and Georg Rueck from the Institute for Experimental Mathematics, Duisburg-Essen University, and the Mathematics Department at Kassel University and there is regular exchange by both staff and students. There is also regular contact with coworkers and specialists from Bordeaux, Konstanz, Ulm, Leiden, Philadelphia, Paris, Tel Aviv and Tokyo.

Many of the students from this group have continued their mathematics research overseas, among them Louis Brewis, Paul Joubert and Adam Mohamed, some have have secured interesting jobs in industry and elsewhere, namely John-Paul Harper and Ernest Lötter, while others have continued at universities and in the education sector, among them Sibusiso Mabaso, Jan Groenewald, Kenza Guenda and Ilhem Benzaoui who are now both in Algeria.

PhD and MSc dissertations have been written on a number of topics which include: On towers of function fields over function fields, Endomorphism rings of hyperelliptic Jacobians, Geometric action of the absolute galois group, Automorphisms of curves and the lifting conjecture, Iwasawa theory of elliptic curves, On algebraic geometric and related codes, Studies on factoring polynomials over global fields,

This group encourages strong interaction with AIMS, research work in mainstream pure mathematics and is excited by the application of these areas to applied science.

A biennial conference series in Arithmetic Geometry has been held in Stellenbosch since 1997. Read more.