Research Interests
Understanding the nature of space and time has been a central question for philosophy and physics throughout the centuries. Space time in its classical form underlies the formulations of quantum (field) theory as well as classical gravity. Yet we know today that both theories are incomplete and that classical space time should be replaced by quantum spacetime. With my research I am contributing towards the construction of a consistent theory of quantum gravity and towards an understanding of quantum space time. My work focusses in particular on non-perturbative approaches of quantum gravity and here on how to obtain a theory of quantum gravity valid over all scales. Such a theory of quantum gravity needs to incorporate renormalization concepts in its very construction. Thus my work involves the understanding of renormalization in a background independent context and with it the development of a framework of how to consistently formulate and construct a theory of quantum gravity. I am also developing renormalization techniques and algorithms applicable to quantum gravity models and aim to use these techniques to extract their large scale behaviour. This latter task is a key open problem of many quantum gravity approaches. Its resolution is highly needed as a consistency test and in order to derive falsifiable predictions from quantum gravity. A partial list of subjects I am interested in: -loop quantum gravity and spin foams -discrete geometries and diffeomorphism symmetry -renormalization in background independent theories and tensor network coarse graining -renormalization and tensor network techniques in lattice gauge theories -new notions of quantum geometry derived from topological field theories -topological phases and defects -holographic formulations of quantum gravity -observables in covariant systems and general relativity