We have active research groups in Algebra; Analysis and Mathematical Physics; Geometry; Numerical Analysis and Scientific Computing; Optimisation; Theoretical Numerical Analysis; and Probability Theory and Mathematical Statistics. Many projects have applications in the natural sciences and further afield: examples include analytic and numerical treatments of partial differential equations; the use of models from Stochastic Analysis in Financial Mathematics; signal processing and data analysis; and fractal geometry and analysis. The Algebra, Analysis, Geometry and Statistics groups are national competence centres and internationally recognised, and cooperate on a regular basis with universities in Europe, the USA, Australia, China and Japan. In addition, research projects funded by the EU, the German Research Foundation (DFG), the German Academic Exchange Service (DAAD) and the Alexander von Humboldt Foundation bring scientific guests to Jena from many countries. In the past years we have conducted international summer schools, workshops and conferences in the Jena region with great success.

The chairs of Analysis, of Theoretical Numerical Analysis and of Geometry are members of the Research Training Group "Quantum and Gravitational Fields" (DFG *Graduiertenkolleg* No. 1523). The Statistics and Geometry groups constitute the German node of the European Marie Curie network "Deterministic and Stochastic Controlled Systems and Applications". With two separate projects in the Priority Programme "Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory" (DFG *Schwerpunktprogramm* No. 1489) the Algebra group is a significant centre for Computer Algebra; moreover the Algebra group also has two separate projects in the Priority Programme "Representation Theory (DFG *Schwerpunktprogramm* No. 1388). The chairs of Theoretical Numerical Analysis and of Scientific Computing are involved in the Priority Programme "Mathematical methods for extracting quantifiable information from complex systems" (DFG *Schwerpunktprogramm* No. 1324) and the Collaborative Research Centre "Gravitational Wave Astronomy" (DFG *Sonderforschungsbereich Transregio* No. 7) respectively. Furthermore, Mathematical Statistics is involved in the International Max Planck Research School for Global Biochemical Cycles.