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

扭曲理论诞生于罗杰·彭罗斯爵士的直觉，即时空不是物理学的基本领域。相反，基本的舞台是扭曲的空间，物理学的时空公式是涌现的。扭曲空间的数学结构，其中光线而不是时空点起主导作用，为一些最基本的物理理论，如广义相对论和规范理论，提供了一个理想的家园。最初的想法是，理论物理中的重要问题，特别是量子引力问题，将通过扭曲空间中的物理定律的公式来澄清。和许多伟大的思想一样，扭扭理论在数学和物理学上向着不同的方向发展，这是最初的发明者没有预料到的。在数学方面，其强大的方法已被应用于微分几何和积分几何，微分方程的分析和表示理论。在物理方面，它在广义相对论和量子场论中的应用，由于存在于扭曲空间中的弦理论的概念，以及最近认识到扭曲变量简化了某些粒子散射实验的描述，而得到了新的推动。这种广泛的应用为不同研究团体之间的跨学科合作提供了完美的基础。

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.