Research Topics

• Computational Science Center A central research topic in the Computational Science Center is the mathematical modeling of various imaging modalities and the reconstruction of the corresponding imaging parameters. Since these imaging methods are by their nature measuring the parameters only indirectly by detecting their effects on some observable quantities (such as ultrasound waves or light beams), the recovery of the desired physical quantities typically leads to ill-posed inverse problems, so that a stable solution often requires a well-adapted regularisation of the problem. Reconstruction algorithms for the problems are then fine-tuned in close cooperation with partners from experimental sciences, within the CD Laboratory MaMSI and the SFB programme Tomography Across the Scales, for example, to work well with real data.

• Applied Harmonic Analysis. The various researchers working on applied harmonic analysis focus on time-frequency analysis, sampling theory, statistical signal processing, music information analysis, phase retrieval, numerical solvers of high-dimensional problems, high-dimensional biomedical data analysis, dimensionality reduction, deep learning, wavelet theory, statistical mechanics, and applied stochastics.

• Machine Learning The research of the Machine Learning group focuses on mathematical and statistical foundations of modern Deep Learning methods, particularly in conjunction with applications in the natural sciences (medicine, computational chemistry, material science, animal breeding). These applications speak to the interdisciplinary nature of the Machine Learning group which has close ties to the Research Network Data Science of the University of Vienna.
• Optimization The working groups in Optimization work on the mathematical modeling, the development and the analysis of discrete and continuous time methods and numerical algorithms for solving high-dimensional smooth and nonsmooth optimization problems as well as on various applications thereof. It is also in charge of the FWF funded PhD programme (Doktoratskolleg)  Vienna Graduate School on Computational Optimization.
• Quantum Information The research in Quantum Information focuses on the study of entanglement, i.e. genuinely quantum correlations in complex quantum systems. This involves on the one hand the mathematical modeling and the numerical simulation of complex quantum systems using entanglement-based descriptions such as tensor network states, and on the other hand the utilization of quantum many-body systems in the construction of quantum computers, as well as a use case for near-term quantum devices.

Research Groups

• Applied Mathematics with Emphasis on Optimization
• Applied Harmonic Analysis Cluster
• Global Optimization
• Inverse Problems
• Machine Learning
• Mathematical Data Science
• Quantum Information