GRK 2088:  Discovering structure in complex data: Statistics meets Optimization and Inverse Problems

• Subject Area: Mathematics
• Term: from 2015 to 2024
• Website: Homepage
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 257660731

The efficient extraction of significant information from complex data is one of the grand challenges in applied sciences. Our research work in the RTG 2088 aims at developing new mathematical concepts for efficient identification, extraction and utilization of relevant structural information in data sets. One of the guiding principles of this RTG consists of discovering and rigorously exploiting structural a priori information in data. We study a wide range of a priori knowledge – such as topological and metric structures, shape space morphology, sparsity in adaptive dictionaries or geometric curvature functionals – to design numerically and statistically stable and efficient algorithms for the extraction and classification of information. Methodologically, we focus on an interplay between approaches in statistics, optimization, and inverse problems. Important solution concepts include generalized regularization techniques, multi-scale methods in harmonic analysis and statistics, statistical inference for topological structures, nonlinear local and global spectral dimensionality reduction, and iterative algorithms at the interface of stochastics and optimization. Within the first funding period, several new important connections between the PhD projects have emerged. Our goal in the second funding period is to deepen and exploit these synergies in order to derive new approaches for data structure analysis and utilization that significantly improve the existing methods. New topics involve for example the theory of averaging operators for random function iterations, new parametric methods to analyze non-stationary signals, or the use of concentration inequalities in nonparametric regularization theory. Most of the proposed PhD projects investigate and further develop mathematical methods with a direct application in biology, medicine or engineering. The RTG has developed an interdisciplinary qualification program which equips our graduate students with a broad set of skills and versatile tools for analyzing data also beyond the scientific scope of the RTG. This provides targeted preparation for successful careers both in academia or industry. The PhD program “Mathematical Sciences” at the University of Göttingen, puts special emphasis on international scientific exchange which is achieved by a visitor program geared towards research and education and by the support of extended research visits abroad for graduate students.

• DFG Programme: Research Training Groups
• Applicant Institution: Georg-August-Universität Göttingen
• Spokesperson: Professorin Dr. Gerlind Plonka-Hoch
• Participating Researchers: Professor Dr. Thorsten Hohage; Professor Dr. Stephan Huckemann; Professorin Dr. Tatyana Krivobokova; Professor Dr. David Russell Luke; Professor Dr. Axel Munk; Professor Dr. Dominic Schuhmacher; Professorin Dr. Anja Sturm; Professor Dr. Matthew Tam; Professor Dr. Max Wardetzky