The Institute of Mathematics consists of 14 research groups researching and teaching about various aspects of mathematics.

## Algebraic Geometry, Topology and Number Theory

**Algebraic Geometry**(van Straten, Ruddat)**Arithmetic Geometry**(Blickle)**Computer Algebra**(de Jong)**Homotopy Theory**(Rahn)- Motivic homotopy theory (Bachmann)
**Topology and Geometry**(Lehn, Hog-Angeloni)**Number Theory**(Müller-Stach, Pfister)

The Research Group Number Theory is currently working on period numbers and period domains. A special focus is the theory and geometry of Shimura varieties.

## Analysis

**Applied Analysis**(Rendall, Fröhlich, Kraus, Schneider)

The group 'Applied Analysis' is concerned with applications of analysis both outside and within mathematics. Key topics are mathematical biology and differential geometry.**Functional Analysis**(Kostrykin, Tolksdorf)

## Didactics of Mathematics

## History of Mathematics and Natural Sciences

In our group, we study the emergence and development of mathematical and

scientific concepts and theories in their respective historical and

cultural contexts.

## Numerical Mathematics

This group represents all facets of numerical analysis, ranging from modelling aspects to scientific computing. Specific research questions include partial differential equations, in particular hyperbolic conservation laws, inverse problems and numerical linear algebra, adaptive discretization schemes and numerical optimization. Applications arise from fluid dynamics, soft matter physics as well as medicine and biology.

## Probability and Statistics

We are concerned with mathematical modelling and analysis of randomness. Our research focus is on interacting particle systems, branching processes, stochastic analysis, statistics of stochastic processes, applications in population- and neuro-biology and in statistical physics.