de Sitter quantum gravity: advances and challenges

<!--HTML--><p>In this colloquium we will review recent progress in de Sitter quantum gravity, with a focus on two directions: de Sitter solutions in String Theory, and holography. In the first direction, we will discuss energetics arguments that give necessary ingredients for obtaining cosmological solutions. We will then argue that M-theory compactified on a hyperbolic manifold, with Casimir energy and flux, gives a simple and promising candidate for 4-dimensional de Sitter spacetime. In the second part of the talk we will discuss how a novel class of controlled irrelevant deformations in quantum field theory are key for a holographic formulation of de Sitter and an explanation of its entropy.</p>