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Explore critical phenomena and phase transitions on S^2 x R space-time geometry using the fuzzy sphere regularization in this 45-minute conference talk. Delve into the application of this scheme to the quantum version of the 3D Ising phase transition, examining its demonstration of state-operator correspondence in conformal field theory. Learn about the efficient extraction of complete conformal data, including scaling dimensions and operator product expansion coefficients, with many previously unknown results. Discover how this innovative fuzzy sphere approach can be extended to study other phase transitions, offering new perspectives on critical phenomena in theoretical physics.