# Research

Research on many fronts of fundamental physics ranging from quantum gravity over quantum field theory (QFT) to cosmology has revealed a striking convergence of ideas and methods. These developments have uncovered deep mathematical structures, such as generalizations of differential geometry, algebraic and number theoretic aspects of scattering amplitudes as well as hidden symmetries and dualities in string theory. The challenges posed by unifying and advancing these research frontiers call for a coherent training program.

The IMPRS for Mathematical and Physical Aspects of Gravitation, Cosmology and Quantum Field Theory aims at establishing such a training program at the interface between physics and mathematics. Its scientific focus encompasses some of the most exciting research avenues in the mathematical description of physics at the smallest and the largest scales. It is now widely accepted that the deepest questions in modern cosmology and particle physics require a consistent quantization of the gravitational field. Recent efforts in this direction have revealed a remarkable confluence of mathematical structures across a wide field of topics. In particular, physicists working in the above areas need expertise in differential geometry, number theory and various branches of modern algebra. Conversely, modern mathematics greatly benefits from physicists' insights. This cross-fertilization will be implemented and strengthened by the PhD projects in the following four related core areas: