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## Researcher

# Karim Johannes Becher

- Research interest:In my research team we study algebraic structures such as rings and fields. These structures are used to deal with arithmetic questions. Arithmetic here means Number Theory in a broad sense. In the first place we want to decide the solvability of certain polynomial equations over fields.This involves methods from algebra, algebraic geometry, algebraic number theory, topology and modeltheory, but also analysis, combinatorics and graph theory. Furthermore we try to describe the complexity of certain structures defined over fields by obtaining bounds for the number of parameters that are needed for describing them.

- Keywords:ALGEBRA, NUMBER THEORY, Mathematics

- Disciplines:Algebraic geometry , Associative rings and algebras , Field theory and polynomials , Linear and multilinear algebra, matrix theory, Number theory

- Research techniques:We apply classical techniques and methods of research in fundamental mathematics. The research is crucially supported by discussion of problems and of preliminary solutions within the research team and with guest and other experts and the detailed preparation and scrutinising of texts which explain the results and proofs. Computations by computer play a smaller role.

- Users of research expertise:Mathematicians, students, researchers from other disciplins dealing with arithmetic problems.