Algebra, algebraisk geometri og topologi (AGATA)

Algebra originates from the study of equations and polynomials.
From this, a rich variety of modern algebraic structures has emerged. Groups, fields, rings, and Lie algebras are among the most fundamental. Algebra becomes especially interesting when it interacts with other fields such as combinatorics, topology, geometry, computational methods, or physics.

In Algebraic Geometry, geometric objects with algebraic structure are studied: Curves, surfaces, and higher-dimensional manifolds that can locally be described by polynomial equations. There is a rich interplay with modern abstract Algebra, Topology, and Complex Analysis. Some of the problems are classical and go back as far as two hundred years, while others are, for example, related to problems in modern theoretical physics.

Topology is the mathematical study of space. In Topology, we are concerned with symmetry and geometry. The objects we study are called topological spaces and include anything with a geometric aspect. The main tools for studying topological spaces are algebra, geometry, and combinatorics. One type of topological space that is related to physical theories such as relativity and string theory is Riemannian manifolds. These are topological spaces equipped with geometric structure, which gives meaning to concepts such as distance, angle, and volume. Roughly speaking, one can say that these are spaces that can be "lived in" in the same way we live in a three-dimensional space.