Shape dynamics is a new, completely relational description of gravity. This description is derived from first principles which implement the observation that all objective observables in physics are ratios between physical objects and locally available reference quantities. The theory provides a different understanding of the nature of gravity: no longer described as a geometrical block of spacetime but as the temporal evolution of spatial conformal geometry. Such an understanding clears major obstructions to the construction of quantum gravity theories, e.g. the nature of observables and their evolution. The methods of the theory bear strong connections to the mathematics of the initial value problem of GR, and to studies of dissipative dynamical systems. Since shape evolution is blind to certain types of singular behavior of the gravitational field, the study of cosmological and local evolution acquires new possibilities. Moreover, Its distinct theory space opens new opportunities for the application of effective field theory treatments and renormalization group methods. This conference brings researchers in these areas together to foster new interdisciplinary discourse and collaboration in this fascinating interplay between conformal symmetry, cosmology, and gravitational physics.