Supergravity and Symmetries
Many remarkable properties of physical models can be traced back to the existence of some underlying symmetry. This applies to systems that differ by many orders of magnitude in scale from for example the Kepler problem of planetary motion to the Standard Model of elementary particle physics. Often these symmetries are "hidden" in the sense that they are not immediately visible in the equations.
Models for quantum gravity that arise from string theory or supersymmetric theories of gravity ("supergravity") can also display hidden symmetries in certain set-ups. It is the principal aim of my research to understand the emergence of these hidden symmetries as the reflection of an inherent symmetry of the equations in a more general context.
Problems addressed in on-going research include finite- and infinite-dimensional symmetries of classical gravity systems, discrete symmetries in quantized models, constraints on perturbative and non-perturbative effects from symmetries and the construction of solutions by symmetry methods. One of the most fascinating questions is to study the consequences of the algebraic and number theoretic structures for the quantum nature of geometry.