In the past couple of days I have been visiting Oxford and then Cambridge, during which I gave one seminar in each place, and an extra talk in an informal journal club in Oxford which was meant to be a pedagogical introduction to the formulation of tree-level amplitudes based on scattering equations. Both seminar talks focus on our recent two papers (arXiv:1409.8256, arXiv:1412.3479) which extended the application of the above mentioned formulation to various theories of massless particles.
Some highlights are that, starting with only two very simple objects (functions of kinematics data and a set of variables parametrizing an auxiliary Riemann sphere with marked points) together with three operations on them, we managed to find out closed formulas for amplitudes in Yang-Mills coupled to gravity (including the well-studied pure gluon amplitudes and pure graviton amplitudes), Einstein-Maxwell, Dirac-Born-Infeld, U(N) non-linear sigma model, and a very special type of the Galileon theory. Furthermore, these new formulas indicates very amusing similarity and connections among amplitudes in these different theories, some of them relatively well-understood from the normal point of view from Kaluza-Klein while others remaining more or less unclear (as of the current status).
The slides for the Oxford talk can be found here.
Due to some change of plan, I switched to a blackboard talk in Cambridge. Most of the contents are similar to that in Oxford, except for a slightly extended review on the general formulation, which can be found here.
In the same file, there is also an additional page related to an update on the Galileon theory that I discussed in the Cambridge talk. In short, the Galileon theory that we identified with one of the new formulas turns out to be a special class of Galileon theories that possess an enhanced symmetry. More discussions on these can be found in paper by Hinterbichler and Joyce (arXiv:1501.07600) late last week.