Brief overview of the research field
Algebra examines the basic structures that occur in mathematics. Many problems from geometry and number theory can be described in new ways with the help of algebraic methods. This leads to surprising and very successful solution methods. Here, the focus is on classification problems.
In four working groups, the entire spectrum is covered: from theory to the construction and the analysis of surfaces and curves, as well as practically oriented computer algebra. Central issues in algebraic geometry include the investigation of properties such as symmetries and structures of surfaces and curves, or the study of varieties; these have important applications in physics, among other areas.
All four working groups are closely linked to the Collaborative Research Center SFB-TRR 195 Symbolic Tools in Mathematics and their Application.