Research at the Department of Mathematics

The analysis, explanation and creation of continual processes, is one of the corner stones of mathematics. This very broad area of research incorporates analysis, differential equations, dynamics, and modelling and supports intensive interaction between the many fields of application.  (more)

Algebra draws its methodology from an interaction between theory, algorithmics and experimentation. The algorithmic aspects today are beoming increasingly significant. For example, algebra is now used in  important areas such as cryptography. (more)

Numerics and scientific computing form the essential foundations for applied, computer- supported mathematics.  Hereby, models, algorithms and software are developed and analysiert, in order to solve problems in ther areas of natural, engineering, and business science.  (more)

Stochastics are an essential part of a modern university.  Because statistics and probability theory are so multifaceted in their applications – from finance and business maths, to material sciences or the modeling of quantum systems. At the TUM, this field of research is linked strongly to analysis and numerics. (more)

The world is geometry! Because in order to understand the world, we often need to recognise the fundamental connections between objects. In our department, the research fields in geometry are manifold, encompassing polytope theory, discrete differential geometry and topology, as well as geometric invariant theory. (more)

Optimization of discrete and continual structures is one of the fundamental tasks in mathematics. In many areas, deeper structural mathematical connections must first be discovered and then analysed. Therefore, optimisation lies on the interface between pure and applied mathematics. (more)

Avoiding financial risks, improving insurance products, optimizing investment strategies, modelling, money flow and quantification of credit risks. To do all this, we use stochastic models, statistic processes und numerical methods. Finance and Insurance Mathematics are fascinating - just like (financial) life itself. (more)

Quantum science provides a fundamental framework for physics, chemistry, and information-processing. Studying systems from small to large, ordered or unordered, open or closed, abstract or applied, we are interested in the unimagined possibilities quantum theory has in store for us. (more)

The discovery of DNA triggered a rapid development in biology and medicine. Many of the achievements in Life Science are  (also) based on mathematics: decryption of the genome, understanding of gene regulation, epigenetics – all this is not possible without mathematics.  (more)

Many applications give rise to data sets of increasing size. As a consequence, new mathematical tools are required for their analysis. We develop and analyze methods for data processing and extracting relevant information, which specifically address the challenges of large data sets. (more)

Mathematics is a fundamental pillar of Computational Science and Engineering (CSE). It provides the models, theory and simulation algorithms essential for predicting future events, for design and optimization of complex systems, and for making critical decisions affecting society. (more)

A picture says more than a thousand words. To transform abstract connections or data into pictures is the work of mathematical visualization.   In the other direction, imaging reconstructs the underlying information captured in a picture. Both are mathematical disiplines which require interconnected thinking. (more)