**Title: **The Geometry of Relative Locality

**Abstract:** In this talk I will describe the fundamental tension that forbids us in my view to reconcile gravity with the quantum. I will explain how this tension forces us to profoundly revise the concept of locality and that this can be done by letting go of the hypothesis of Absolute locality. I will formulate what relaxing this hypothesis means and will describe our attempts to flesh out the concept of relative locality. I will also exemplify what relative locality is into specific examples. In particular, we will show how these ideas allows us to natural interpret geometrically the T-duality symmetry of string theory. This symmetry will be seen as relativistic change of frame in a modular space, a notion of space that replaces Minkowski for quantum geometry. I will also show how the geometry of relative locality is intimately linked with generalized geometry and the geometry of quantum mechanics via a natural structure on phase space called Born geometry. Finally, and if time permits, I will comment how relative locality can shade a bright new light on the problem of unification. This talks involves several new important concepts: relative locality, generalized geometry, modular space, Born geometry. I will try to present them in a non technical manner as much as possible.

*In terms of technical difficulty, this talk rates 4/5.*

PP Nov15 Freidel flyer