Alday-Maldacena duality and AdS Plateau problem
  A short summary of approximate approach to the study of minimal surfaces in AdS, based on solving Nambu-Goto equations iteratively. Today, after partial denunciation of the BDS conjecture, this looks like the only constructive approach to understanding the ways of its possible modification and thus to saving the Alday-Maldacena duality. Numerous open technical problems are explicitly formulated throughout the text. 
A.Morozov