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Explore the path integral formulation of pure 3D gravity on finite spacetime regions through this 45-minute conference talk by Thomas Hartman from Cornell University, presented at the Institute for Advanced Study's Workshop on Quantum Aspects of Black Holes and Spacetime. Discover how boundary conditions that fix dihedral angles or geodesic lengths enable the calculation of black hole matrix element statistics in dual conformal field theory. Learn about the connection between fixed-length path integrals and Virasoro topological quantum field theory, and examine the fixed-angle path integral as the partition function of Conformal Turaev-Viro theory—a novel topological theory based on triangulations. Understand how these two approaches are related through a modular S-transform, providing new insights into the quantum gravitational structure of three-dimensional anti-de Sitter spacetime.
