Since the start of the First grant in March 2009, I would divide my main findings in three big categories : the physics of extremal black holes, the application of string theory to cosmology and the application of holography ideas to flat space and strongly coupled condensed matter systems.
In the context of black holes, I have a constituent model for certain extremal non-supersymmetric ones explaining their main macroscopic properties. This is analogous to identifying the "molecules" of a gas in a room for these gravitational objects. Furthermore, I showed that the quantum dynamics of these "molecules" is governed by a very specific set of quantum field theories : two dimensional chiral conformal field theories (CFTs). I showed these arise as infinite momentum limits of standard non-chiral CFTs used in statistical mechanics and condensed matter. I have made these discussions very precise when these black holes are small.
In the context of cosmology, I developed a computer algorithm to identify the subset of spaces where to compactify string theory to connect it to the real world. The main constraint used so far is to make sure such space allows a vacuum compatible with what we see without going beyond the regime of validity of the methods being used. These results have triggered a better analytical description of the mathematical properties these spaces require.
In the context of holography, I have explored the use of the famous Anti deSitter-CFT correspondence conjectured in string theory to describe strongly coupled real laboratory systems such as Luttinger liquids, including their interactions with fermions. I have definite statements regarding the stability of these systems and their phase space structure as a function of the different physical parameters. Furthermore, I have proposed some preliminary extension of these holographic ideas to flat space, by identifying what the relevant symmetries are and what kind of quantum mechanical theories realise them.