I will provide a general introduction to tensor models and their applications to quantum gravity. Initially developed in the context of random geometry, as a generalization of the matrix models approach to 2d quantum gravity, tensor models and their large N expansion have more recently been taken advantage of in the context of holography. In particular, the "near AdS_2 / near CFT_1 correspondence" establishes a connection between strongly-coupled and explicitly solvable large N quantum mechanics and Jackiw-Teitelboim gravity in d=2.

The conformal bootstrap aims to systematically constrain CFTs based on crossing symmetry and
unitarity. In this talk I will introduce a new approach to extract information from the crossing symmetry
sum rules, based on the construction of linear functionals with certain positivity properties. I show
these functionals allow us to derive a class of optimal bounds on CFT data, and also act as an ideal basis
for obtaining other bounds numerically. Furthemore I will argue that special extremal solutions to

Until now, observations and experiments have confirmed General Relativity (GR) as the best theory of gravity. The current gravitational wave interferometers, LIGO and Virgo, as well as the future space-based detector LISA, will permit to challenge further GR in the highly dynamical and strong field regime of gravity. In this talk, I will focus on alternative theories with an additional scalar degree of freedom, in relation to compact objects.