We discuss the initial boundary value problem in general relativity (with vanishing cosmological constant). We consider a non-standard set of boundary conditions, known as conformal boundary conditions, where the conformal class of the induced metric and the trace of the extrinsic curvature are fixed at the boundary. We compare these results with analogous results for the Dirichlet problem both in Lorentzian and Euclidean signature, where a notion of conformal black hole thermodynamics will be developed. Time permitting, we will discuss implications for holography and de Sitter space.

In these lectures, we will present to seemingly different theories. The first one is a theory of gravity in two dimensions, called Jackiw-Teitelboim (JT) gravity, that is relevant in the context of higher-dimensional, near-extremal black holes. The second one is a quantum mechanical theory of fermions, with no gravity, called the Sachdev, Ye and Kitaev (SYK) model. We will explore precisely how JT gravity emerges from the SYK model by studying their actions, correlation functions and thermodynamic properties. This constitutes the simplest toy model of what theoretical physicists now call the holographic principle. Address: 21 Albemarle St, London W1S 4BS Floor 2: London Institute of Mathematical Sciences (LIMS)

In these lectures, we will present to seemingly different theories. The first one is a theory of gravity in two dimensions, called Jackiw-Teitelboim (JT) gravity, that is relevant in the context of higher-dimensional, near-extremal black holes. The second one is a quantum mechanical theory of fermions, with no gravity, called the Sachdev, Ye and Kitaev (SYK) model. We will explore precisely how JT gravity emerges from the SYK model by studying their actions, correlation functions and thermodynamic properties. This constitutes the simplest toy model of what theoretical physicists now call the holographic principle. Address: 21 Albemarle St, London W1S 4BS Floor 2: London Institute of Mathematical Sciences (LIMS)

In these lectures, we will present to seemingly different theories. The first one is a theory of gravity in two dimensions, called Jackiw-Teitelboim (JT) gravity, that is relevant in the context of higher-dimensional, near-extremal black holes. The second one is a quantum mechanical theory of fermions, with no gravity, called the Sachdev, Ye and Kitaev (SYK) model. We will explore precisely how JT gravity emerges from the SYK model by studying their actions, correlation functions and thermodynamic properties. This constitutes the simplest toy model of what theoretical physicists now call the holographic principle. Address: 21 Albemarle St, London W1S 4BS Floor 2: London Institute of Mathematical Sciences (LIMS)

In these lectures, we will present to seemingly different theories. The first one is a theory of gravity in two dimensions, called Jackiw-Teitelboim (JT) gravity, that is relevant in the context of higher-dimensional, near-extremal black holes. The second one is a quantum mechanical theory of fermions, with no gravity, called the Sachdev, Ye and Kitaev (SYK) model. We will explore precisely how JT gravity emerges from the SYK model by studying their actions, correlation functions and thermodynamic properties. This constitutes the simplest toy model of what theoretical physicists now call the holographic principle. Address: 21 Albemarle St, London W1S 4BS Floor 2: London Institute of Mathematical Sciences (LIMS)

Cosmological (or de Sitter) horizons behave qualitatively different to black hole horizons and this poses a challenging problem in the context of holography. In this talk, I will discuss a novel construction to probe de Sitter horizons using the usual tools of the AdS/CFT correspondence. I will further explore ongoing efforts to reconstruct the bulk metric in two dimensions from the dual quantum mechanical correlators in the boundary.