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I am currently working on questions related to the AdS/CFT duality.
This duality is a conjecture, which relates a 4-dimentional field theory (called N=4 Super Yang-Mills) and a string theory on the curved space AdS5xS5. It is up to now the best understood example of a duality between gauge and string theories, and it maps the strong coupling regime of one theory to the perturbative (weak coupling) regime of its dual theory.
This property (that a perturbative regime is dual to a strong coupling regime) make this duality all the more usefull, but also the harder to check, making it necessary to use powerful mathematic tools, such as the integrability (which I have been studying).
Up to now, I have worked on the integrability of spin chans, but also for the spectrum of fields theories (expressed by means of a Thermodynamic Bethe Ansatz, under the form of a "Y-system"). More specifically, a universal object called Q-operator, was an impressive tool for my work on these subjects.
Among the question I am interested in, one big challenge is to get a better understanding of the structure (namely T-operators and Q-operators with very specific analitycal properties, which are currently understood only in the setup of the thermodynamic Bethe ansatz). Other questions (such as amplitudes computations) can be tackled due to integrability, and I am interested in them as well. Moreover, in case this webpage is not completely up to date, you can have a look at my articles, which will give you an idea of the evolution of my research areas.