Computing bulk microstates

<!--HTML--><p>A central question in AdS/CFT is how the string degrees of freedom are organized in the dual gauge theory. In my talk, I present an exact formula that relates the BPS sectors of U(N) gauge theories and their string duals. The formula expresses the finite N superconformal index of a U(N) gauge theory as a sum over stacks of bulk giant graviton branes. I explain how to holographically construct the indices of bulk string/brane configurations by analyzing the modifications of determinant operators in gauge theory. Finally, I discuss implications for black holes and the bulk BPS Hilbert space. Based on 2109.02545 and 2204.09286</p>