## Mathematics in Kaiserslautern

Top international research - from theoretical foundations to real industrial applications

With its research focusses in

- Algebra, Geometry and Computer Algebra,
- Analysis and Stochastics,
- Industrial Mathematics and
- Economathematics,

the Department of Mathematics has prioritized attractive scientific and socially relevant areas. This and its current mathematical proficiency establish a sound basis for being nationally and internationally competitive. There is hardly a place where the modern self-understanding of mathematics is lived and pursued as consistently as in Kaiserslautern:

Mathematics is not only (indispensable) fundamental science but a (if not the) key technology of the 21st century.

Algebra, Geometry and Computer Algebra

The Algebra, Geometry and Computer Algebra Group (AGAG) focusses on fundamental research in classical key areas of pure mathematics and on modern applications thereof.

Analysis and Stochastics

This research focus links two of the core areas of mathematics: analysis and stochastics. In research, we study analytic, stochastic and geometrical problems, combining theoretical and application-oriented, algorithmic aspects. Deterministic and stochastic models of continuous mathematics are developed and systematically analysed.

Economathematics

The research focus Economathematics (Wirtschaftsmathematik) is distinguished by fundamental research in the areas Mathematical Optimization, Financial Mathematics, Stochastic Control, and Statistics as well as by interdisciplinary research projects.

Industrial Mathematics

In its research profile, the research area Industrial Mathematics focuses on the modelling, analysis and numerical simulation of differential equations, and also on their optimization and control.

Most research groups of the faculty closely collaborate with departments of the Fraunhofer ITWM. The well-established networking and inter-institutional research cooperation of the Department of Mathematics and the Fraunhofer ITWM has been documented by the foundation of the Felix Klein Center for Mathematics. Thanks to the combination of the widely recognized and outstanding research programs of the department of mathematics, and the open-to-the-world and practically oriented projects of the Fraunhofer ITWM, the Felix Klein Center will undoubtedly strengthen the position of Kaiserslautern in the field of mathematics.

The option of experiencing mathematics in all its facets - from abstract, purely theoretical basic research to real industrial applications - and in an internationally oriented environment makes Kaiserslautern extremely attractive for talented students as well as scientists from Germany and abroad.

The Collaborative Research Center "Symbolic Tools in Mathematics and its Application" (SFB-TRR 195) of the German Research Foundation (DFG), established in 2017, has set itself the goal of significantly advancing research in the field of computer algebra systems in order to be able to answer fundamental mathematical questions by using these systems.

As part of the SFB-TRR 195, scientists of the Algebra, Geometry and Computer Algebra group (AGAG) cooperate with research groups at RWTH Aachen University, Saarland University, and TU Berlin as well as at the Universities of Siegen, Stuttgart and Tübingen.

Working groups from all four research focusses are significantly involved in strategic projects within the framework of the research initiative of the state Rhineland-Palatinate. The focus is on two initiatives:

MathApp – Mathematics applied to real-world challenges, whose goal is the development of new, cross-area mathematical methods and models with relevance for real life applications.

SymbTools – Symbolic Tools in Mathematics and their Application. The main topic here is the development and application of algorithmic methods and computer algebra software which merge the areas of algebra, geometry and number theory and which can be used as versatile tools in mathematics, science and technology.