Research in MATH+ is multifaceted and comprises project-oriented, and project-independent mathematics research. The project-oriented research in MATH+ is structured into Application Areas (AA), Emerging Fields (EF), Incubator Projects (IN), and the Transfer Unit (TrU), and focuses on application-oriented mathematics. On the other hand, the research activities in the eight mathematical research areas in MATH+ are not restricted to the classical form of a project and aim at the progression in mathematics itself.

The MATH+ Application Areas are tailored toward mathematical research in interdisciplinary application fields. They support cross-institution research projects that involve mathematicians as well as leading experts of the respective field of application. The following Application Areas are currently running:

The Emerging Fields are devoted to pioneering interdisciplinary research in new fields including the social sciences and humanities.The following Emerging Fields are currently running:

The Transfer Unit is designed for translational research with industry. Further details can be found here.

MATH+ Incubator Projects are short-term 12-months projects expected to have a high potential impact within the Topic Development Lab by advancing fundamental mathematics or build new bridges within mathematics or with closely related disciplines.

Further details can be found here.

The present mathematical research areas are:

- Differential geometry, global analysis, and mathematical physics
- Algebraic and arithmetic geometry, number theory
- Stochastics and mathematical finance
- Discrete mathematics and optimization
- Geometry, topology, and visualization
- Numerical analysis and scientific computing
- Applied analysis and differential equations
- Mathematics of data science

The MATH+ Spotlight talks aim to strengthen the connections between ongoing research projects in MATH+ and keep MATH+ members up to date with what’s currently happing in the Cluster. They are meant to foster relations between and across Applications Areas and Emerging Fields as well as Incubator and Transfer projects. At the same idea, BMS Phase I students can get ideas for their dissertation topics. In each talk, the (post) doctoral researchers from the projects shine a spotlight onto their scientific work.

Further details can be found here.

The measures that MATH+ undertakes to support the research data management in its various projects are summarized on a separate page.