Resolution of Singularities in Quantum Gravity and Quantum Cosmology.

奇点是在广义相对论的背景下出现的，比如黑洞和大爆炸。它们标志着经典广义相对论的崩溃，以及为了获得更全面的理解，需要一个量子引力理论。许多理解这些奇点的工作都是在简化模型（超空间模型）中完成的，但这些模型是否能捕捉到全量子引力的相关物理还远不清楚，因为这些模型往往依赖于额外的特别假设，而这些假设的基本理由尚不清楚。我博士的目标是从量子引力理论如群场论（GFT）和环量子引力（LQG）中发展更系统和严格的有效对称约简量子宇宙学模型的推导。特别是，宏观宇宙是从量子几何中大量相互作用的自由度的“凝聚”中获得的想法将被采用。

Singularities arise in the context of general relativity like in black holes and at the Big Bang. They signal a breakdown of classical general relativity and the need for a quantum theory of gravity in order to obtain a more complete understanding. A lot of work for understanding these singularities has been done in simplified models (minisuperspace models) but it is far from clear whether these capture the relevant physics of full quantum gravity as such models often depend on additional ad-hoc assumptions whose fundamental justification is unclear. The goal of my PhD is to develop a more systematic and rigorous derivation of effective symmetry-reduced quantum cosmology models from proposed theories of quantum gravity such as group field theory (GFT) and loop quantum gravity (LQG). In particular the idea that a macroscopic universe is obtained from a "condensate" of a large number of interacting degrees of freedom of quantum geometry will be employed.