Institute of Experimental Mathematics
Universitity of Duisburg-Essen

The core of the activities of the Number Theory Group is research inarithmetic geometry and algebraic number theory. A large part of the research questions are related to the Langlandsprogramme, which is a dominant and very topical subject in number theory. Close connections exist to algebraic geometry, representation theory and other areas of mathematics.

Specific research themes are Shimura varieties, and in particular their reductions in positive characteristics, modular forms and Galois representations, elliptic and hyperelliptic curves, the inverse Galois problem as well as the representation theory of p-adic groups, linear groups and their combinatorics.

A characteristic of the Number Theory Group are the extensive connections between research on up-to-date theoretical research questions and far reaching applications of explicit, algorithmic and experimental methods: Deep insights are often founded on the knowledge of examples that can only be obtained from computer calculations, and on the other hand a profound knowledge of the theory is often fruitful or even indispensible for performing formerly impossible computations and for discovering new applications. In many projects, computer algebra programs are utilised and developed or mathematical problems are studied for explicit computability. Applications exist in particular in the area of data security which comprises cryptography and coding theory.