Theoretical Investigations in Classical and Quantum Gravity

在广义相对论引力、广义相对论与量子物理学的统一以及这些理论在宇宙学中的应用等领域将完成若干项目。这项研究旨在加深我们对黑洞动力学，早期宇宙物理学，与时空结构相关的基本问题，如黑洞内部是否丢失信息，时空的量子性质，古典空间的出现时间从量子几何和广义相对论的接口和量子力学的基础。这项研究预计将产生更广泛的影响，它将提供：一）新的工具，从黑洞等强引力系统的数值模拟中提取可靠的物理内容;二）大爆炸附近时空的量子性质产生的宇宙学新投入;三）分析广义相对论的动力学和完全非线性状态的严格基础，这对引力波的天体物理源很重要; iv）量子力学的基础;和v）对数学领域的贡献，如几何分析，量子群理论和全纯结构的应用。

A number of projects will be completed in the areas of general relativistic gravity, unification of general relativity with quantum physics and applications of these theories to cosmology. This research is aimed at deepening our understanding of the dynamics of black holes, physics of the early universe, fundamental issues related to space-time structure such as whether information is lost inside black holes, quantum nature of space-time, the emergence of classical space-times from quantum geometries and the interface of general relativity and the foundations of quantum mechanics.This research is expected to have a broader impact on related areas because it will provide: i) new tools to extract reliable physical content of the numerical simulations of strongly gravitating systems such as black holes; ii) new inputs into cosmology arising from the quantum nature of space-time near the big-bang; iii) a rigorous basis for analyzing the dynamical and fully non-linear regime of general relativity which is important for astrophysical sources of gravitational waves; iv) foundations of quantum mechanics; and v) contributions to a areas of mathematics such as geometric analysis, theory of quantum groups and applications of holomorphic structures.