de Sitter vacua in String Theory @ICTP, Italy.
In 1998, two independent observations showed a most unexpected fact about our universe: it is accelerating. Our best model of particle physics and gravity predicts that the universe should be accelerating, but at a rate that is significantly larger than what is observed. The quantum fluctuations of the fields that permeate space give a contribution to the energy density of the vacuum (the so-called cosmological constant) that is naturally close to the quantum gravity scale, the Planck scale. The observed value lies some 122 orders of magnitude below the Planck scale. The puzzle is not why the cosmological constant is there, but why it is so incredibly small.
This is perhaps the most important problem in theoretical physics today, and since the monumental discovery of 1998 little to no progress has been made. One avenue of research I was involved in while at ICTP was to derive the small value of the cosmological constant from string theory models. String theory predicts 6 extra dimensions other than the 3 usual ones that we perceive in every day life, and the precise shape of the extra dimensions influences the physics we see in our 3D universe. You can think of the geometry of this extra space as providing the "DNA" for the world we observe. The laws of Nature are encoded in the morphology of the extra dimensions.
The genetic diversity of possible universes is quite astonishing. Different compactification manifolds in the extra dimensions give wildly different values for the vacuum energy (and other parameters, like the mass and coupling of the particles). No single value emerges from the theory, but rather a huge number of them, and the value that we measure locally can only be argued for by a selection effect. We live in a very special universe where the cosmological constant is small but non-zero because that is conductive to our existence. Other values simply cannot be observed because they correspond to universes devoid of observers. This is the controversial anthropic principle, and its string theory realization, the Landscape.
For the nerds, my work consisted in the Kähler moduli stabilization and computation of the moduli masses in an explicit type IIB orientifold compactification in the LARGE volume scenario. The Calabi-Yau manifold we studied had been recently proved to support a nilpotent goldstino, an essential ingredient in obtaining a dS minimum. I wrote my Master thesis on this at ICTP.