Many of the most challenging problems in science and engineering involve physical systems that evolve over time while exhibiting rich mathematical structure. Fluid flows, reactive materials, biological systems, plasmas, and complex engineered processes are governed not only by differential equations, but also by geometric constraints, conservation laws, symmetries, and interactions across multiple spatial and temporal scales. Developing mathematical representations that faithfully preserve this structure is one of the central challenges in modern scientific computing.
At Eindhoven University of Technology, we are launching a new research programme that aims to develop the mathematical foundations for next-generation Digital Twins: computational representations of physical systems that preserve geometric structure, physical consistency, and mathematical invariants throughout their evolution. Our vision combines ideas from differential geometry, numerical analysis, scientific computing, dynamical systems, and applied mathematics to develop new mathematical frameworks for representing, compressing, and computing with complex physical systems. The project is carried out in close collaboration with researchers in Electrical Engineering working on emerging memory architectures and novel computing paradigms, providing a unique opportunity to contribute to mathematics with a clear technological impact.
We are recruiting two complementary postdoctoral researchers to join this programme. While both positions contribute to the same overarching research vision, candidates may have expertise in different areas of mathematics.
One position will focus primarily on geometric and structure-preserving methods for mathematical models of physical systems, including topics such as geometric numerical integration, finite-volume and finite-element methods, variational formulations, structure-preserving discretisations, optimal transport, and the numerical analysis of partial differential equations.
The second position will focus primarily on the geometric representation of complex data and physical systems, including topics such as differential geometry, invariant theory, algebraic and metric geometry, symmetry, geometric data analysis, and infinite-dimensional geometric structures.
The two postdoctoral researchers will work closely together, together with professors Rafael Bailo and Mireille Boutin, to develop mathematical theories that connect geometric models of physical systems with new computational representations suitable for Digital Twins and future computing architectures. The project offers substantial freedom to develop original mathematical ideas while contributing to a coherent long-term research programme at the interface of geometry, analysis, scientific computing, and computational mathematics.
The two postdoctoral researchers will be expected to undertake a modest teaching load.
