**Lecture 1: Tuesday, 13 August 2024 at 16:00 hrs**

**Title: **Entanglement and emergence of gravitational spacetime

**Abstract: **Recently, a new interpretation of gravitational spacetime in terms of quantum entanglement has been developed. The idea of holography in string theory provides a simple geometric computation of entanglement entropy. This generalizes the well-known Bekenstein-Hawking formula of black hole entropy and strongly suggests that a gravitational spacetime consists of many qubits with quantum entanglement. Also a new progress on black hole information problem has been made recently by applying this idea. A new insight on holography for de Sitter spaces have also been obtained from quantum information viewpoints. I will explain these developments in this lecture.

**Lecture 2: Wednesday, 14 August 2024 at 10:30 hrs**

**Title:** Gravity duals of CFTs on manifolds with boundaries

**Abstract: **AdS/CFT correspondence has played crucial roles to understand difficult problems in quantum gravity in terms of quantum field theories. When a conformal field theory (CFT) is defined on a manifold with boundaries, we can generalize the standard AdS/CFT by introducing so called end-of-the-world branes. This extended holographic duality, called AdS/BCFT, captures, for examples, the essential feature of quantum gravity such as the black hole information problem. In this lecture, I would like to explain how this holographic duality works and discuss recent developments.

**Lecture 3: Friday, 16 August 2024 at 10:30 hrs**

**Title: **Pseudo entropy and de Sitter Holography

**Abstract:** Pseudo entropy is an interesting quantity with a simple gravity dual, which generalizes entanglement entropy such that it depends on both an initial and a final state. In this talk we start with an introduction of this new quantity explaining its basic properties and its holographic calculations. Next, we will present recent numerical results of this quantity in a free scalar field theory and in a spin system, which imply that pseudo entropy can serve as a new quantum order parameter. Finally, we will discuss an application of pseudo entropy to holography in de Sitter spaces and to entanglement phase transitions.

**About the speaker**: Tadashi Takayanagi is a professor at Yukawa Institute for Theoretical Physics, Kyoto University. After he completed his Ph.D. in Tokyo University in 2002, he worked for four years as a postdoc at Harvard and KITP. He was an assistant professor at Kyoto University and an associate professor in Kavli IPMU, Tokyo University, before he moved to his current position in 2012. He has been awarded the Yukawa-Kimura Prize in 2011, the Nishinomiya-Yukawa Memorial Prize in 2013, the New Horizons in Physics Prize in 2014 and the Nishina Memorial Prize in 2016. Takayanagi ’s main research contributions have been studies of quantum entanglement by using holography and quantum field theories. In particular, he discovered a holographic formula for entanglement entropy in 2006 with Shinsei Ryu. He has contributed to developing this idea to relate gravitational spacetimes and quantum information from various methods, until now.

This lecture is part of the program "Quantum Information, Quantum Field Theory and Gravity".