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Explore a groundbreaking "CFT factory" algorithm that systematically generates 2D lattice models flowing to conformal fixed points in the infrared through this 48-minute conference talk. Learn how to construct critical 2D models by applying specific boundary conditions to 3D topological orders described by string-net models, utilizing non-commuting anyon condensates to achieve criticality. Discover the role of "refined condensation trees" in controlling non-invertible symmetries at critical points and understand how this structured approach produces an infinite family of critical lattice models, including A-series minimal models and previously unknown critical points. Examine novel critical points with c≈1.3, 1.8, and 2.5 that preserve Haagerup symmetries, alongside the recovery of previously reported ones. Master the use of condensation trees combined with generalized Kramers-Wannier duality to predict phase boundaries and determine global phase diagrams while identifying second-order phase transitions. Study applications to well-known examples like the 8-vertex model related to the A5 category and explore verification through precision numerics using improved non-invertible symmetry-preserving tensor-network renormalization group methods. Understand how critical couplings encode categorical data including Frobenius algebras and quantum dimensions in unitary fusion categories, establishing a systematic pathway for discovering and potentially classifying new conformal field theories.
