Arithmetics, Algebra and Discrete Mathematics

The key research area Arithmetic, Algebra and Discrete mathematics comprises research groups in algebraic structures and group theory, in number theory, in algebraic geometry and commutative algebra, and in combinatorics.

Group theory is pursued mainly from a geometric and analytic point of view. Here, algebraic and probabilistic techniques are combined, for example, with methods inspired by mathematical physics.

In Number theory, it is the Langlands Program, which lies at the core of our research. The Langlands Program is a still expanding web of several deep conjectures and results, relating different objects in arithmetic, geometry and analysis. This entails strong connections with algebraic geometry and also with combinatorics.

In Algebraic Geometry, research directions include enumerative and combinatorial algebraic geometry, and approximation techniques in commutative algebra. We also study resolution of singularities,  projective varieties via graded ring methods, moduli spaces and mirror symmetry.

In the area of Discrete mathematics, a broad spectrum of combinatorial themes is investigated and developed that ranges from algebraic combinatorics to analytic combinatorics and graph theory. Consequently, there are strong interrelations with algebra, number theory, and also with statistical physics.

Research groups

• Algebraic geometry and Kommutative algebra
• Algebraic structures and Group theory
• Discrete Mathematics and Combinatorics
• Number theory