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 information

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

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

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

The world is geometry! Because in order to under­stand the world, we often need to recognize 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 information

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 analyzed. Therefore, optimization lies on the interface between pure and applied mathematics. More information

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 and numerical methods. Finance and Insurance Mathematics are fascinating - just like (financial) life itself. More information

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 information

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 information

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 information

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 information

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 disciplines, which require interconnected thinking. More information