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 Xn+Yn=Zn. 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.