Inspiration corner is a bunch of CDs that the guys would listen to when they were making a new album. For SFAM, they had Sgt. Pepper, Tommy, the Wall, and a few other concept albums. For SDOIT, the only one I remember was Tool's AEnima. For BC&SL, they were all DT albums.
Not really sure what the new inspiration corner for this album would be. Mike was the one who really liked to talk about what he listened to. James has been talking a lot about his musical tastes as well, like Radiohead, Soilwork, Queen, Coheed & Cambria, and Killswitch Engage. Whether any of those bands show up in an inspiration corner or if there even IS an inspiration corner remains to be seen. I mean, they haven't even gone into the studio yet

Personally, I hope they do away with the inspiration corner, whether it was just a Mike idea or not.