Generalized Geometry and Symmetries
The unification of Einstein's theory of general relativity with quantum physics represents one of the greatest challenges of modern theoretical physics. A hypothesis common to all research directions aiming at understanding the quantum theory of gravity is that our description of space-time geometry has to go beyond the classical picture of space-time as a differentiable manifold. Within this project we are interested in generalized concepts of geometry, physically motivated by string theory: generalized complex geometry and non-commutative geometry. We aim at improving our understanding on how these generalized notions of geometry could be utilized to obtain consistent extensions of symmetry principles. In particular, we are interested in extending the gauge principle, the key physical notion used to describe all (known) matter interactions, in view of the above generalizations of classical geometry. Our goal is to capture the effects of string duality symmetries, non-commutative gauge theory and higher gauge theories at the level of the effective field theory description, which is necessary in order to perform reliable calculations and yield experimentally testable predictions. We expect that geometrizing these generalized symmetries would provide us, as a long-term perspective, with a consistent framework within which one could address open issues in cosmology and black-hole physics.