**Zoom virtual seminar: click here to enter room**

**Abstract**: I will discuss the superconformal index that counts states preserving two supercharges in N=4 SYM, and more generally in N=1 SCFTs, on S^3. This index is captured by a unitary matrix model with purely double trace operators in the action. The AdS/CFT correspondence predicts that the index should have exponential growth at large charges and large N, corresponding to the 1/16-BPS black hole (BH) in AdS5. I will present analytical and numerical analyses of the matrix model which clearly show this expected BH growth. In particular, I will introduce a deformation of the matrix model which allows us to solve it at large-N. The deformation has interesting relations with the Bloch-Wigner dilogarithm, a function introduced by number theorists.

Finally, using techniques from representation theory, I will show that the finite-N index actually interpolates between counting multi-gravitons at small charge and BHs at large charge.