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The ERC Consolidator Grant project Computational Complexity of Highly Nonlinear Approximations (COCOA) will fund several postdoctoral and PhD positions at RWTH Aachen. The positions will be available from July 1st, 2025. We are in particular inviting applications for a PhD position. The project will investigate numerical methods for high-dimensional partial differential equations, such as parameter-dependent problems, Fokker-Planck and Schrödinger equations, based on nonlinear approximations such as low-rank tensor decompositions, Gaussian mixtures and neural networks, with a particular focus on the computational costs of reliable solvers. Candidates for the PhD position should have solid knowledge of analysis and numerics of PDEs and interest in pursuing one of the above topics. The position will be part of the Institute of Geometry and Applied Mathematics (IGPM), which offers a vibrant research environment in applied mathematics with strong connections to other research projects, such as the DFG CRC Sparsity and Singular Structures. All positions are remunerated according to TV-L E13 (100%). Contracts for the PhD positions can extend for up to 4 years. To apply, please send your application documents to Markus Bachmayr (bachmayr@igpm.rwth-aachen.de). These should include CV with contact details of at least two references, list of publications, statement of research interests, certificates and transcripts, and copies of (or links to) previous work such as BSc or MSc theses. Applications will be considered until the position is filled. Informal inquiries are welcome.