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Explore the fascinating intersection of black hole physics and cohomology theory through this 35-minute mathematical physics lecture. Delve into supercharge Q-cohomology in holographic quantum field theories and discover how it characterizes microstates of supersymmetric black holes in dual quantum gravity scenarios. Learn how these concepts generate compelling cohomology problems using N=4 super-Yang–Mills (SYM) theory as the primary framework. Examine how the existence of supersymmetric black holes in gravity duals leads to the prediction of novel cohomology classes and challenges established conjectures regarding the relationship between cyclic cohomology and Lie algebra cohomology. Gain insights into cutting-edge research that bridges advanced mathematical concepts with theoretical physics, particularly in the context of holographic duality and supersymmetric systems.
