Mathematical Data Science and Artificial Intelligence

On the one hand, the research group develops the mathematical principles necessary to understand modern AI systems—while also creating methods that make AI more robust, explainable, and trustworthy. The chair combines mathematics, computer science, and statistics, investigating both the mathematics of AI and AI for mathematics. Areas of application range from inverse problems and partial differential equations to medical imaging and robotics. In addition, the chair supports interdisciplinary projects on security, transparency, and regulatory compliance—for example, in the context of the EU AI Act—as well as projects on novel hardware-software approaches.

On the other hand, the research group focuses on the mathematical foundations of machine learning—in particular, deep learning—as well as signal and image processing. Key topics include the convergence behavior of (stochastic) gradient methods, the generalization properties of neural networks, and the theory of compressed sensing for data-sparse reconstruction. This research is based on high-dimensional probability theory, optimization, and harmonic analysis.

Through the close interconnection of its research topics, the working group creates a coherent research framework that combines mathematical rigor with the demands of modern AI, thereby advancing both basic research and innovative applications.