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Twistor theory was originally proposed by Roger Penrose as a geometric framework for physics that aims to unify general relativity and quantum mechanics. In this approach, spacetime is secondary with events being derived objects that correspond to compact holomorphic curves in a complex three--fold, the twistor space. The mathematics of twistor theory goes back to the 19th century Klein correspondence in projective geometry, but one of the unexpected spinoffs from twistor theory is its impact on modern pure mathematics, from differential geometry and representation theory to gauge theories and integrable systems. Loop quantum gravity is a background-independent approach to the quantization of general relativity. It provides a compelling picture of quantum spacetime in terms of a collection of `atoms’ with discrete spectra, and the possibility of resolving the singularities of general relativity. Applied to cosmology and black hole physics, it has led to new ideas for the origin of the universe (a `Big Bounce’ replacing the Big Bang) and the final state of Hawking evaporation. The communities working in these two theories share both technical and a conceptual pillars, however they have evolved independently for many years, with different methods and intermediate goals. Some recent developments have weaved a possible new path of interaction: Collaborations between researchers in the two fields have started, with the potential to enrich each other and find new synergies. The aim of the proposed meeting is to bring together for the first time the two communities in a broad and comprehensive way, to strengthen this interdisciplinary overlap and foster new collaborations and developments, concentrating primarily on the geometric and general– relativistic aspects. Leading international researchers both in twistor theory and loop quantum gravity will have the opportunity to establish and consolidate the connections between the two areas of research, and to overcome problems at the forefront of both fields.