The research focus of pure mathematics in Augsburg comprises several chairs, whose research covers a wide range of basic-oriented mathematics.

In the field of algebra, current questions of algebraic and complex geometry, logical foundations of modern mathematics and the theory of D modules are examined. The focus of the research is on hyper-chaeler manifolds, higher category theory, synthetic geometry, Stokes structures of irregular D-modules with regard to irregular Riemann-Hilbert correspondences.

The Chair of Analysis and Geometry (with mathematical physics) deals with applications of modern symplectic geometry to Hamiltonian dynamics, especially in connection with celestial mechanics. A particular focus is the study of periodic pathways, their connection with the topology of the loop space and their importance for the design of space missions.

At the Chair of Differential Geometry, we deal with the topology and geometry of manifolds. For this purpose, methods of algebraic and geometric topology, higher category theory, differential geometry and global analysis are used. In current research, algebraic K theory and questions of scalar curvature geometry play a central role.

A close linkage between the individual research directions and joint scientific activities create an inspiring environment for students and young scientists.

For associated professors see German version.

Augsburger Applied Mathematics deals with mathematical questions from the natural, life and engineering sciences. The aim is to describe real phenomena with the help of mathematical models, to understand them theoretically and to simulate them efficiently with numerical methods — up to the use of high-performance computers and quantum computers. Many of these questions arise in the context of interdisciplinary projects; accordingly, Applied Mathematics maintains close ties to the CAAPS.

Special expertise lies in the modeling, analysis, the treatment of inverse problems and the numerics of problems on the continuum scale – often also on several scales, such as microstructured materials. Application-related questions usually require the interaction of several, often even all of these areas. It is precisely this combination of theory, algorithms and application that characterizes Augsburg’s Applied Mathematics.

The focus area optimization and data science bundles research and teaching on modern mathematical methods for data-driven questions. These are equally examined from a theoretical, algorithmic and application-oriented perspective.

In the field of mathematical optimization, discrete and continuous optimization problems are investigated in the same way as nonlinear and combinatorial optimization problems. Both global and linear, semi-definite and conical optimization play a role, as do methods of mixed-integer optimization. Applications in the field of operations research such as the sustainable deployment planning of bus fleets are also being investigated. This results in a variety of connections to adjacent areas of discrete mathematics, for example to combinatorics, graph theory and coding theory.

In the field of data science, a variety of aspects are considered, such as statistical learning, data analysis and efficient algorithms for large and complex data volumes. This profile is complemented by research on tensor-based methods, high-dimensional approximation and powerful optimization algorithms. Mathematical image processing is also at the centre of research in the field of data science.

Through the close integration of theory, algorithms and application, the focus area optimization and data science offers an attractive environment for interdisciplinary research as well as for a well-founded, future-oriented education of students in dynamic and socially highly relevant research fields.

Stochastics – this is the mathematics for the analysis of random systems. In Augsburg, we research stochastics in theory and practice.

Our theoretical research is devoted to random processes, random media and random graphs. The focus is on the study of universal phenomena that appear in a variety of application areas. A central guiding question is to what extent their macroscopic behavior can be derived from the microscopic properties of large systems and how the dynamics of collective phenomena — for example in financial and insurance markets — can be understood.

Another mainstay is the application of mathematical research for statistical data analysis. With research partners in industry and clinics, we develop new mathematical methods, for example for modeling electricity markets, for the optimal use of battery storage and for the improvement of medical treatments. Essential tools are computer-intensive data processing methods and methods of artificial intelligence.

For associated professors see german version.

The didactics of mathematics deals with the teaching and learning of mathematics at all ages. In Augsburg, teaching mathematics for primary school, middle school, secondary school and high school can be studied. The training is consistently practice-oriented and focuses on the mathematical content that should be taught, as well as on the associated ideas and possible misconceptions of the learners.

In research, we deal, among other things, with the influence of technology (e.g. computer algebra systems or artificial intelligence) on learning as well as with the application of mathematics to non-mathematical problem areas, for example in the context of education for sustainable development.

For associated professors see german version.