# Research Areas

At the Institute for Algebra, in addition to applications, we focus on fundamental research. The following areas, among others, are being examined intensively:

## Universal algebra

Manuel Bodirsky, Reinhard Pöschel

The central concern of universal algebra is the classification of general algebraic structures. Tools for this are function clones and invariant relations, equation logic and varieties. An important application of universal algebra lies in the theory of the complexity of constraint satisfaction problems.

## Model Theory

Manuel Bodirsky, Arno Fehm

Model theory is a branch of mathematical logic and deals with properties of classes of algebraic structures (e.g. groups, graphs, fields) and their relationship to formal (syntactic) properties of the associated theories. Research in this area at the Institute for Algebra focuses on homogeneous structures and their automorphism groups as well as the model theory of fields.

## Number Theory

Arno Fehm

The classical field of number theory, according to C. F. Gauss the "queen of mathematics", deals in the broadest sense with properties of whole numbers. Number theory in Dresden focuses on Galois theory and its applications, number theory in function fields and Diophantine geometry.