This troupe has a national profile partly because of its participation in the reality TV show "Breaking Pointe," which chronicled the personalities and backstage antics of this Salt Lake City company. For its Joyce Theater debut, the troupe will keep the drama onstage in New York premieres by Matthew Neenan and Nicolo Fonte as well as Val Caniparoli's "The Lottery," based on Shirley Jackson's chilling short story about a violent ritual in a small town. Helen Pickett, resident choreographer of the Atlanta Ballet, contributes a world premiere.