The interplay between mathematics and theoretical physics has a long tradition in Leipzig and is connected to names like that of the 1932 Nobel Prize Laureate Werner Heisenberg. In the years following the German reunification, the late Max Planck Founding Director Eberhard Zeidler kept this tradition alive and his efforts finally culminated in the foundation of the Max Planck Institute for Mathematics in the Sciences, in 1996. The fruitful collaboration at the interface of mathematics and theoretical physics in several research projects as well as in the joint international Max Planck doctoral school IMPRS (International
Max Planck Research School Mathematics in the Sciences). After its foundation in 2005, the IMPRS has established itself as a renowned graduate school, and more than 90 doctoral students have graduated on topics at the interface of mathematics and the natural sciences.
Building on this tradition, a new joint initiative of our Institute together with Leipzig University aims at strengthening existing cooperations between the Institute and the Physics and Mathematics Departments at the University of Leipzig. The scientific focus of the collaboration is centered around the groups "Pattern Generation, Energy Landscapes and Scaling Laws" led by the Max Planck Director Professor Felix Otto and "Elementary Particle Physics" of the Institute for Theoretical Physics led by Professor Stefan Hollands.
The scientific focus is broadly on the investigation of systems whose dynamics have a random component. The random influences can be very different in nature, such as thermal noise or quantum effects. Accordingly, the mathematical methods are very versatile and range from the theory of differential equations to techniques that can be used to describe the dynamics of systems at different length and time scales.
The project will initially receive funding for five years from the Max Planck Society and the University of Leipzig. Dr Paweł Duch, the first of up to five scientists, ha already been hired for this project and joined our institute at the beginning of October. Paweł received a PhD in physics in 2017 from the Jagiellonian University, Poland, where he worked on mathematical aspects of quantum field theory, scattering theory, and classical general relativity. He considers physics as a source of interesting mathematical problems and recognizes the importance of mathematical rigor in theoretical physics. In Leipzig, he intends to be working on problems at the interface between quantum field theory and stochastic partial differential equations.
This initiative only as a first step to further develop Leipzig into a center of mathematical physics, attracting young talents interested in this interdisciplinary research area. The initiative is flanked by an international M.Sc. degree course in mathematical physics at the University of Leipzig, which is planned for the next year.
Scientific background of the project leaders Felix Otto and Stefan Hollands:
Felix Otto's expertise are Partial Differential Equations, the language in which practically all major theories in physics are formulated. For instance, he has been working on the effective behavior of random media, which for instance plays a role in groundwater flow and oil recovery, where the porous medium is only known in terms of its statistics. In mathematical terms, this leads to Partial Differential Equations with random coefficients, defining a fluctuating geometry.
The scientific interests of Stefan Hollands lie at the interface between General Relativity and Quantum Field Theory. While General Relativity describes gravity in terms of the curvature of space-time and other geometric properties, Quantum Field Theory relies on the notion of fields to describe elementary particles and their interactions. A particularly interesting setting in which to investigate the relation between Quantum Field Theory and General Relativity are physical systems in which space-time curvature has a significant impact on the quantized excitations, for example in the vicinity of black holes as well as at "the beginning" of the universe. Quantum Field Theory is not only interesting as a physical theory, but also continues to pose exciting and fruitful challenges to Mathematics, opening up new avenues for connections with very diverse fields within this subject.