Colloquium

The covariant formulation of loop quantum gravity has developed strongly during the last few years.  I summarize the current definition of the theory and the results that have been proven. I discuss what is missing towards of the goal of defining a consistent quantum theory whose classical limit is general relativity.

Mass, a concept familiar to all of us, is also
one of the deepest

mysteries in nature.  Almost all of the mass in the
visible universe,

you, me and any other stuff  that we see around us, emerges from a

quantum field theory, called QCD, which  has a completely negligible

microscopic mass content. How does QCD and the family of
gauge

theories it belongs to  generate a mass?



This class of non-perturbative problems remained largely elusive despite much

Entropy plays a fundamental role in quantum information theory through applications ranging from communication theory to condensed matter physics.  These applications include finding the best possible communication rates over noisy channels and characterizing ground state entanglement in strongly-correlated quantum systems.  In the latter, localized entanglement is often characterized by an area law for entropy.  Long-range entanglement, on the other hand, can give rise to topologically ordered materials whose collective excitations are robust against local noise.

Black holes lead a double life, simultaneously the dark, enigmatic, hairless consequence of general relativity and the powerful engines lurking at the hearts of galaxies with cosmological consequences.