Our group shall push the envelope of non-perturbative calculations in quantum field theories, unravel the geometry of the inner space that controls our observable reality, and determine the shape and fate of quantum spacetime with an eye towards new models for real-world physics. To this end we shall make crucial use of the two innovations of non-invertible symmetries and quantum localisation. More explicitly: we shall introduce for the first time a theory of non-invertible symmetries in quantum nonabelian Chern-Simons theory, and leverage it to solve the closely-related problems of gauged worldsheet interfaces as well as of nonabelian string dualities beyond tree-level; we shall initiate the study of string theory compactifications with U-duality patchings and their attendant physical consequences, as well as the study of U-duality induced topology change; and we shall advance an ambitious programme of exact calculations in (non-)supersymmetric field theories, beginning with the immediate example of three-dimensional gauge theories of Yang-Mills type, with an eye towards exact results for quantum chromodynamics in four dimensions.