Collaborative Research Center: Sparsity and Singular Structures

 

We are part of the DFG-funded Collaborative Research Center "Sparsity and Singular Structures", which combines the expertise of several mathematicians at RWTH Aachen University from the fields of analysis, probability theory, numerical analysis, optimization and algebra.

The CRC focuses on mathematical foundations for complex models and high-dimensional data in science and technology with an emphasis on simulation and machine learning. A guiding principle is the identification and exploitation of algebraic, geometric and analytic structures that appear in underlying mathematical problems or in mathematical solution concepts and algorithms.

We make a significant contribution to the project group "Singular and geometric PDEs." Singular structures such as point defects and interfaces lend themselves as starting points for developing new concepts of sparsity in applied analysis and at the crossroads with numerical analysis. Our projects involve singular harmonic maps and flows, Mullins-Sekerka evolution, and Ginzburg-Landau vortices in the Gross-Pitaevskii equation.