(non physicist, non mathematician) The current excitement seems to be to do with a forthcoming paper from Arkani Hamed and his student Jaroslav Trnka. The pdf at http://www.staff.science.uu.nl/~tonge105/igst13/Trnka.pdf has some details of that, I think.

Edit to add:

The pdf is slides from a talk by Trnka. Video of a later talk on the same topic by Arkani Hamed is at http://susy2013.ictp.it/video/05_Friday/2013_08_30_Arkani-Ha... - he sounds very excited!