Tensor models: from random geometry to holography

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.

A more functional bootstrap

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

Dark energy from quantum gravity discreteness

I will argue that discreteness at the Planck scale (naturally expected to arise from quantum gravity) might manifest in the form of minute violations of energy-momentum conservation of the matter degrees of freedom when described in terms of (idealized) smooth fields on a smooth spacetime. In the context of applications to cosmology such `energy diffusion' from the low energy matter degrees of freedom to the discrete structures underlying spacetime leads to the emergence of an effective dark energy term in Einstein's equations.

Probing scalar-tensor theories with compact binaries

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.

Primordial black holes and the inflationary universe

The interest in primordial black holes (PBHs) has recently risen up 
again after the discovery of around 30 solar mass black holes through 
the LIGO/Virgo gravitational wave events. PBHs are black holes produced 
by gravitational collapse of the over-dense region in the early universe.
 An attractive origin of the overdensity is primordial perturbations 
generated during inflation. In this talk, I will first explain the 
relation between the power spectrum of the perturbations predicted by 


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