Explore the fascinating world of topological states of matter in this 48-minute lecture on the theory of disorder-induced half-integer thermal Hall conductance. Delve into the fractional quantum Hall effect, examining exchange statistics in 2D and 3D systems, and the rich landscape of quantum states. Learn about the quantization of heat flow in fractional quantum Hall regimes, experimental techniques for measuring thermal conductance, and the intricacies of hole-conjugate states. Investigate the behavior of complex fractions, temperature dependencies, and the implications for non-abelian states at v=5/2. Gain insights into cutting-edge research on topological phases of matter and their potential applications in condensed matter physics.