Quantum fields interacting with geometry – QFG

The main aim of the project is the application of techniques from partial differential equations, microlocal analysis and scattering theory to the study of quantum matter interacting with spacetime geometry. The last decade has witnessed spectacular progress in the mathematical description of phenomena in relativistic physics. However, one of the great persisting challenges is to understand how does the presence of quantum matter alter the Einstein equations (and therefore, the geometry), and how do the dynamics of spacetimes give rise to quantum effects. This is a strong impulse for exploring topics including scattering theory of gauge fields, quantization of linearized gravity and renormalization problems in relation with PDEs and Lorentzian geometry, with the ultimate objective of establishing a rigorous formulation of theories where quantum degrees of freedom interact with gravity.