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 

Transport effects due to quantum anomalies

Anomalous transport phenomena emerge in systems where quantum anomalies break certain classical symmetries leading to nonconservation of associated, and otherwise classically conserved, currents. In backgrounds of magnetic or gravitational fields, as well as in rotating systems, the anomalies may generate nondissipative flows of energy and charge currents even in the presence of strong interactions. We review recent theoretical developments on the anomalous transport in systems possessing axial, axial-gravitational, and conformal anomalies.

Hamiltonian vs stability in alternative theories of gravity

When a Hamiltonian density is bounded by below, we know that
the lowest-energy state must be stable. One is often tempted
to reverse the theorem and therefore believe that an unbounded
Hamiltonian density always implies an instability. The main
purpose of this talk is to pedagogically explain why this is
erroneous. Stability is indeed a coordinate-independent property,
whereas the Hamiltonian density does depend on the choice of
coordinates. In alternative theories of gravity, like k-essence
or Horndeski theories, the correct stability criterion is


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