Workshop "Twistor Theory and Beyond", 29 June - 1 July 2020, Cambridge

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Twistor theory was born out of Sir Roger Penrose's intuition that space-time is not the fundamental arena of physics. Instead, the fundamental arena is twistor space, and the space-time formulation of physics is emergent. The mathematical structure of twistor space, where light-rays rather than space-time points take the leading role, provides an ideal home for some of the most fundamental theories of physics, such as general relativity and gauge theory. The original idea was that important problems in theoretical physics, especially the problem of quantum gravity, would be clarified by a formulation of the laws of physics in twistor space.As with many great ideas, twistor theory developed in a variety of directions in mathematics and physics, which were not anticipated by its original developers. On the mathematical side, its powerful methods have been applied to differential and integral geometry, to the analysis of differential equations and to representation theory. On the physics side, its application to general relativity and quantum field theory has been given a renewed impetus with the notion of string theories living in twistor space, as well as with the recent realisation that twistor variables simplify the description of certain experiments in particle scattering.This vast range of applications provides a perfect ground for interdisciplinary collaboration among diverse research communities.