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Explore a high-energy theory seminar that delves into quantum cosmology in 2+1 dimensions, focusing on simple, solvable models where precise statements can be made due to the absence of local degrees of freedom. Learn about two key findings: first, examine cosmological solutions with negative cosmological constant and torus-shaped spatial slices, where cosmological observables connect to boundary conformal field theory observables, particularly the relationship between cosmological amplitude and CFT density of states. Then investigate positive cosmological constant cosmology, discovering the exact spectrum of the static patch Hamiltonian through path integral methods, revealing a bounded spectrum with integer degeneracy in certain cases. Understand how the inclusion of both positive and negative norm states contributes to finite de Sitter entropy, aligning with the Bekenstein-Hawking entropy of the de Sitter event horizon, including precise numerical coefficients.
