# Welcome to the Discrete Biomathematics work group!

Mathematics, by its universal nature, is nowadays intertwined with a wide variety of disciplines, such as physics, economics, social or life sciences. Phrasing a problem in rigorous mathematical terms often allows for a high-level understanding and opens the way for structured analysis. In turn, problems and questions found in applications have the potential to spark profound mathematical questions of interest. This is particularly true for mathematical biology, where researchers are confronted with highly complex systems spanning many scales in time and space.

Within this group we are interested in modeling and analysis approaches for biological networks using discrete and hybrid methods and the mathematical questions motivated by the applications. In the context of systems biology we are are particularly interested in molecular signaling networks as they play an important role in understanding diseases such as cancer, tackling questions concerning modeling, analysis and control. Looking beyond networks acting in single cells we are working on mathematical approaches that allow to capture multi-cell models and enable us to investigate the phenomenon of pattern generation. Testing our understanding of the underlying mechanisms of complex systems can be done by following an engineering approach as is done in synthetic biology, another area we are active in. Lastly, we are interested in evolutionary processes on different scales, tracking biodiversity changes through deep time using temporal networks and genetic changes by analyzing phylogenetic trees. Overall, we are aiming at accompanying this interdisciplinary work with innovative connections within mathematics, enriching our core domain in discrete mathematics by touching on continuous and stochastic dynamical systems theory, formal verification and machine learning as well as algebraic approaches. For more information, see Research and Projects.