Non-perturbative aspects of three-dimensional quantum gravity

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This project will focus on various non-perturbative aspects of three-dimensional quantum gravity. It will cover cases with positive (dS) and negative (AdS) cosmological constant. Tools that will be used are related to AdS/CFT, the Chern-Simons formulation of the theory, and exact methods in two-dimensional conformal field theories. For AdS, the overarching aim is to construct a gravitational path integral and find a result that describes a unitary quantum theory. For dS, one aspect is to quantify the Hartle-Hawking wave function of the universe, and test the stability of quantum de Sitter space.