The research interests of the Department of Mathematics can be divided into the main areas of algebra and number theory, geometry and topology, geometric analysis, differential equations and calculus of variations, numerical mathematics and scientific computing, discrete mathematics and mathematical optimization as well as stochastics and insurance mathematics . These research areas are closely linked and often overlap. For example, geometric and topological methods are used in algebra and number theory, while the modern concepts of stochastics open up new perspectives on problems in analysis.

The department is actively involved in third-party funded projects such as DFG-funded programs (e.g. SFB TRR 191, SPP-1335, SPP 2265) and has received two UoC Forum grants. It is also involved in BMBF projects and collaborations with industrial partners and has acquired a large amount of funding, including various ERC grants and DFG individual fellowships. There are also close research collaborations with other departments at the university, in particular with the geosciences, physics and medicine.