Each module consists of 6 hours of lectures + discussion/workshop sessions.

In addition, participants are strongly encouraged to engage in the Gong Show and present their research activity.

Lectures available on YouTube: https://www.youtube.com/channel/UCf0rF9SdnfU-NpUSst6t1wg

• Black holes, Supergravity and Holography - Chiara Toldo

These lectures will deal with the thermodynamic and microscopic properties of black holes in Anti-de Sitter (AdS) spaces. I will first review general features of AdS black holes, for instance their thermodynamic stability and their phase transitions. I will then give an overview of the known supersymmetric (and non-supersymmetric) black holes in theories of supergravity and their properties, including pedagogical examples of their construction, and I will highlight some open questions. I will then explain recent progress in retrieving the entropy of supersymmetric black holes via microstate counting in the dual field theory via supersymmetric localization.

• Cosmological Fluctuations and their Bootstrap - Guilherme Pimentel

I will review what we know about the initial conditions of the universe, and show how they are computed and predicted from the framework of cosmic inflation. Then I will focus on the non-Gaussian statistics of these primordial fluctuations, showing how they can be ‘’bootstrapped’’ from symmetry, locality and unitarity. I will mostly present the theory of primordial scalar fluctuations, but time permitting will also say something about tensor fluctuations, which have their own peculiarities. The tools used involve a blend of scattering amplitudes, gauge/gravity duality, and conformal field theories.

• A Primer on Celestial Holography - Prahar Mitra

In these lectures, we will introduce the basics of celestial holography, starting with a discussion of asymptotic symmetries in asymptotically flat spacetimes, Ward identities and soft theorems, and ending with an introduction to celestial CFTs and their structure.

• Twistors, Amplitudes, and Holography - Atul Sharma

Penrose's twistor theory studies four-dimensional gauge theory and gravity with the lens of complex projective geometry. In this course, we will introduce the basics of twistor spaces, with a view toward building toy models of celestial holography in the language of Witten's twistor string theory. Along the way, we will encounter many fashionable words like "scattering amplitudes", "non-linear gravitons", "w(1+infinity) symmetry", "topological strings", etc. that will definitely help you land a job.