driven basic research and a multitude of applications in other disciplines that are also continuously raising new questions and problems. The Faculty of Mathematics, its 29 research groups making it one of the largest in Germany, covers a wide range of these developments and thrives on the ever-surprising interactions sparked by the exchange of mathematical methods and tools between different fields. Questions on the opportunities and challenges that these developments offer regarding mathematics education and educational justice are also part of our research.

The key areas of our research can roughly be divided into four thematic subsections: Algebraic Geometry and Arithmetic, Analysis/Numerical Mathematics and Optimization, Stochastics, and Didactics of Mathematics. The very large number of research projects that were successful in receiving funding from external sources such as the German Research Foundation (DFG), the Humboldt Foundation, the Federal Ministry of Education and Research (BMBF) and the Tele­kom Foundation underscored the importance of the main research interests and reflect the success of organisational changes in the Faculty of a few years ago.

The projects outlined here allowed us to intensify national and international collaboration and organise international workshops, summer schools and conferences. The topics of “System Modelling and Optimization”, “Arithmetic Geometry”, “Evolutionary forces and genealogical trees”, and “STEM teaching of the future” give an initial impression of the range of our research projects.

We are particularly happy that we were again able to attract and support very strong young scientists in the two years of the report. Our Faculty’s 2018 postdoctoral prize was awarded to Dr. Livia Betz for her project “Second-order Sufficient Optimality Conditions for Optimal Control of Non-smooth Semilinear Parabolic Equations” and to Dr. Marcel Klinger for his project on the use and effects of algebra apps and maths teaching in schools and universities (“Computer-Algebra-Apps und Mathematikunterricht: Nutzungshäufigkeit und Auswirkungen in Schule und Universität”).