Over the last few years there has been enormous progress in our understanding of supersymmetric gauge theories. Much of this progress stems from new methods for exact computations in quantum field theories i.e. computing certain observables for all values of the couplings.
Furthermore, supersymmetric gauge theories have proven to have a very rich physical and mathematical structure. This manifests itself in the form of dualities with other theories, in different numbers of dimensions.
We have been especially interested in the exact computation of various observables, such as supersymmetric indices, partition functions, and Wilson loops, and their related observables in the dual theories. This also ties into our work on gauge-gravity duality.
We are also interested in pursuing the conformal bootstrap programme for supersymmetric conformal field theories. This involves the use of using consistency conditions in order to constrain the data for a conformal field theory.