Let's try if the WLAN works -- if you can read this, it does.
The first session I attended this morning was on Theoretical Approaches beyond Quantum Field theory. The first talk there was by Gregory Korchemsky, who spoke about scattering amplitudes in maximally supersymmetric Yang-Mills Theory. Super-Yang-Mills theory is the supersymmetric version of Yang-Mills theory and its maximally supersymmetric version is the most supersymmetric theory one can have that does not include gravity. It describes a fermionic field (the gluinos, which are like quarks, only living in a different representation of the gauge group) interacting with gluons and scalar fields. The theory's symmetries are very powerful and impose tight constraints on its correlation functions -- enough to uniquely determine all tree-level amplitudes from the symmetries alone. In fact, even when considering loop contributions, some of the scattering amplitudes are determined by symmetry, while the others are at least strongly constrained.
The next talk was by Henryk Johansson, speaking about the relationship between gravity and gauge theories at the perturbative level. This approach relies on some very difficult-to-grasp hidden structures that lead to unexpected relations between tree-level amplitudes both within Yang-Mills theory and in YM theory and gravity, that can apparently be lifted to the loop level as well.
This was followed by a talk on monodromies in gauge and gravity amplitudes by Pierre Vanhove. This approach also relies on hidden structures of gauge theory and gravity, and what limited part of it I understood seemed closely related to (what limited part I understood of) the previous talk -- e.g. resolving everything into cubic vertices only.
The last talk of the session was Slava Rychkov, who spoke about constraints on Conformal Field Theories. Again using the symmetries of the theory, he derived bounds on the dimensions of operators and on the OPE coefficients or interaction strengths in CFT. This may have some applications to technicolor theories.
Theoretical high energy physics has become such a hugely diverse field that people working on different areas, even if they explore the same physics (e.g. gauge theories) using different methods (e.g. lattice simulations vs. analytical approaches), speak almost entirely different languages, and it becomes very hard to understand each other's talks; still, it is important to see what progress is being made using other approaches, even if one walks away with the humbling feeling of not understanding all that much.