At the Henry Fonda Theater on Hollywood Boulevard last night, YouTube introduced its new “Screening Room,” an area of the site devoted exclusively to selected independent films. The Screening Room will feature four short films every two weeks, as well as the occasional full-length feature. The first several slates of films are chock-a-block with recognizable names and Academy Award-nominated filmmakers, but as the program continues, YouTube expects to include films submitted to a kind of cinema slush pile, to keep at least a modicum of the “You” in YouTube.