Unification, Quantum Gravity and Noncommutative Geometry

理论物理学中的一个挑战性问题是量子物理定律与爱因斯坦广义相对论的统一。在这个方向上，人们最有力地追求的思想是超弦理论和非对易几何。这两种方法密切相关。非对易几何为研究黎曼几何的标准方法所不能处理的空间提供了一个新的框架。它为规范理论和希格斯场的作用的研究提供了一个新的视角，并且是描述普朗克能量下几何的一个有希望的候选者。该计划的主要重点是研究亚普朗克尺度下的时空性质，并找到其几何性质，从而确定动力学。这项研究的更广泛的影响是，这项研究涉及非对易几何的前沿工作，对物理学家和数学家都有好处。

A challenging problem in theoretical physics is the unification of the laws of quantum physics with Einstein general theory of relativity. The ideas in this direction that have been pursued most forcefully are superstring theory and noncommutative geometry. These two approaches are intimately related. Noncommutative geometry has provided a new framework to study spaces which could not be handled by the standard methods of Riemannian geometry. It offered a new perspective in the study of gauge theories and the role of the Higgs field and is a promising candidate to describe geometries at Planckian energies. The main focus of this proposal is to study the nature of space-time at sub- Planckian scales and to find its geometric properties and thus determine the dynamics. The broader impact of this research is that the research involves work on the frontiers of noncommutative geometry and will be of benefit to both physicists and mathematicians.