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.
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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 aim of these lectures is to introduce these ideas to a beginning PhD student in high energy physics.

The lectures will cover the following topics in succession:
- A review of the basics of black hole thermodynamics
- The ideas underlying the counting of statistical entropy of black holes in string theory
- The appearance of a special class of black holes called BPS black holes for which the statistical entropy can be calculated
- The nature of the corresponding microscopic ensemble of BPS states
- An illustration of the calculation of their statistical entropy in some simple examples.
At the end of these lectures, the student is meant to have gained an orientation with respect to the basic ideas and be equipped with some basic techniques used in microstate counting.

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 aim of these lectures is to introduce these ideas to a beginning PhD student in high energy physics.

The lectures will cover the following topics in succession:
- A review of the basics of black hole thermodynamics
- The ideas underlying the counting of statistical entropy of black holes in string theory
- The appearance of a special class of black holes called BPS black holes for which the statistical entropy can be calculated
- The nature of the corresponding microscopic ensemble of BPS states
- An illustration of the calculation of their statistical entropy in some simple examples.
At the end of these lectures, the student is meant to have gained an orientation with respect to the basic ideas and be equipped with some basic techniques used in microstate counting.

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 aim of these lectures is to introduce these ideas to a beginning PhD student in high energy physics.

The lectures will cover the following topics in succession:
- A review of the basics of black hole thermodynamics
- The ideas underlying the counting of statistical entropy of black holes in string theory
- The appearance of a special class of black holes called BPS black holes for which the statistical entropy can be calculated
- The nature of the corresponding microscopic ensemble of BPS states
- An illustration of the calculation of their statistical entropy in some simple examples.
At the end of these lectures, the student is meant to have gained an orientation with respect to the basic ideas and be equipped with some basic techniques used in microstate counting.

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 aim of these lectures is to introduce these ideas to a beginning PhD student in high energy physics.

The lectures will cover the following topics in succession:
- A review of the basics of black hole thermodynamics
- The ideas underlying the counting of statistical entropy of black holes in string theory
- The appearance of a special class of black holes called BPS black holes for which the statistical entropy can be calculated
- The nature of the corresponding microscopic ensemble of BPS states
- An illustration of the calculation of their statistical entropy in some simple examples.
At the end of these lectures, the student is meant to have gained an orientation with respect to the basic ideas and be equipped with some basic techniques used in microstate counting.