Delve into the first lecture of a three-part series on supersymmetric black holes, the superconformal index, and phases of AdS/CFT correspondence. Explore the microscopic explanation of supersymmetric black hole entropy as a crucial test for quantum gravity theories. Learn about recent advancements in this field within the context of AdS/CFT correspondence, focusing on AdS5/CFT4. Discover how the entropy of supersymmetric black holes in Anti de Sitter space is counted using the superconformal index of four-dimensional superconformal field theory at large N. Examine the identification of supersymmetric black hole solutions as saddle-points in the matrix integral representing the superconformal index, and investigate the generalization to an infinite family of solutions with competing free energies, leading to a complex phase structure. This in-depth lecture, presented by Sameer Murthy from King's College, London, is part of the INFOSYS-ICTS String Theory Lectures series held at the International Centre for Theoretical Sciences in Bengaluru. Read more