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

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.

The extraordinary range of applications of twistor theory is the true testimony of its impact across mathematics and physics. On the mathematical side, its methods have been applied to differential and integral geometry, to the analysis of differential equations and to representation theory. On the physics side, they have been applied to general relativity, quantum field theory and string theory.

The range of the distinguished participants in the workshop will reflect this interdisciplinary character. It is not common that a workshop brings together researchers from such diverse fields. This will allow the participants to benefit from the achievements of twistor methods in other disciplines, and to engage in discussions and collaboration with researchers that they rarely encounter in ordinary work.

The impact goes well beyond the participants. There is a much wider community that benefits from the developments achieved with twistor techniques, while not necessarily being proficient in the use of those techniques.

The UK is the birthplace of twistor theory and of its creator, Sir Roger Penrose. It maintains a very strong expertise in this area. Therefore, British-based researchers are very well placed to benefit from this workshop, and to take advantage of the international collaboration opportunities that will arise. Distinguished researchers from institutes ranging from East Asia to the American Pacific have already accepted our invitation to participate in the workshop.