# Arithmetik & Zahlentheorie

The main problem in number theory is the solution of Diophantine
equations, i.e., of systems of polynomial equations with integer
coefficients. Maybe the best known example is the Fermat equation
X^{n}+Y^{n}=Z^{n}. The structure and study of Diophantine equations is
strongly related to almost all branches of mathematics.
The connections to Analysis (uniform distribution of sequences, theory
of automorphic forms), Algebra (representation theory of algebraic
groups, Diophantine approximation) and Geometry (geometry of numbers,
arithmetic algebraic geometry, theory of motives and Galois
representations) are characteristic for the modern research in
number theory and at the same time a constant source of new
developments.