The superconformal index of N=4 super Yang-Mills theory on a three-sphere is captured by a unitary matrix model with purely double trace operators in the action. The AdS/CFT correspondence predicts that this index should have exponential growth at large charges and large N, corresponding to the 1/16-BPS black hole (BH) in AdS5. I will show how the matrix model gives rise to this expected BH growth as well as an infinite number of new phases. 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. I will then show how this matrix model can be expressed in terms of a system of free fermions in a certain ensemble. Integrating out the fermions and averaging over the ensemble leads to a convergent expansion as a series of determinants, showing how giant gravitons in the dual AdS5 are encoded in the gauge theory. . If you are planning to attend, please send and email to pietro.benetti_genolini@kcl.ac.uk or alan.rios_fukelman@kcl.ac.uk so your name is added to the participants list in order to grant you access to the building.

The pioneering work of Bekenstein and Hawking in the 1970s showed that black holes have thermodynamic properties like temperature and entropy in the quantum theory, just like the air in this room. This leads to the question: can we account for the thermodynamic entropy of a black hole as a statistical entropy of an ensemble of microscopic states? One of the big successes of string theory is to answer this question in the affirmative for a large class of black holes.

The pioneering work of Bekenstein and Hawking in the 1970s showed that black holes have thermodynamic properties like temperature and entropy in the quantum theory, just like the air in this room. This leads to the question: can we account for the thermodynamic entropy of a black hole as a statistical entropy of an ensemble of microscopic states? One of the big successes of string theory is to answer this question in the affirmative for a large class of black holes.

The pioneering work of Bekenstein and Hawking in the 1970s showed that black holes have thermodynamic properties like temperature and entropy in the quantum theory, just like the air in this room. This leads to the question: can we account for the thermodynamic entropy of a black hole as a statistical entropy of an ensemble of microscopic states? One of the big successes of string theory is to answer this question in the affirmative for a large class of black holes.

The pioneering work of Bekenstein and Hawking in the 1970s showed that black holes have thermodynamic properties like temperature and entropy in the quantum theory, just like the air in this room. This leads to the question: can we account for the thermodynamic entropy of a black hole as a statistical entropy of an ensemble of microscopic states? One of the big successes of string theory is to answer this question in the affirmative for a large class of black holes.

Supersymmetric localization is a powerful technique to evaluate a class of functional integrals in supersymmetric field theories. It reduces the functional integral over field space to ordinary integrals over the space of solutions of the off-shell BPS equations. The application of this technique to supergravity suffers from some problems, both conceptual and practical. I will discuss one of the main conceptual problems, namely how to construct the fermionic symmetry with which to localize. I will show how a deformation of the BRST technique allows us to do this. As an application I will then sketch a computation of the one-loop determinant of the super-graviton that enters the localization formula for BPS black hole entropy.

Supersymmetric localization is a powerful technique to evaluate a class of functional integrals in supersymmetric field theories. It reduces the functional integral over field space to ordinary integrals over the space of solutions of the off-shell BPS equations. The application of this technique to supergravity suffers from some problems, both conceptual and practical. I will discuss one of the main conceptual problems, namely how to construct the fermionic symmetry with which to localize. I will show how a deformation of the BRST technique allows us to do this. I will then sketch a computation of the one-loop determinant of the super-graviton that enters the localization formula for BPS black hole entropy.

I will discuss the idea that a black hole in string theory is made up of a large number of microscopic constituents. For a class of black holes and black strings with extended supersymmetry, one has an exact counting formula for the number of states. I will sketch the idea and derivation of some of these formulas. I will then discuss applications to the AdS_2/CFT_1 and the AdS_3/CFT_2 correspondences.

I will discuss the exact quantum entropy of supersymmetric black holes as a gravitational functional integral in AdS2. In theories with eight supercharges, a computation of the exact entropy is possible using supersymmetric localization. I will discuss this technique, and describe the computation of functional determinants that can be computed using index theorems. I will then compare the exact gravitational formula to microscopic formulas coming from string theory.