Usually when Americans think of important ballet companies, their minds go to one of the two major companies in New York City. But these days one of the most influential groups, the Joffrey Ballet, is based only a handful of hours from Columbus. The Joffrey — which moved from New York to Chicago in the mid-’90s — was the first troupe to combine elements of ballet and modern dance, and it was the first ballet company to perform to rock music. The documentary “Joffrey: Mavericks of American Dance” examines how the group revolutionized ballet, and the movie’s screening Saturday at the Gateway will be followed by an interactive webcast with some of the Joffrey’s key players. For those of us who get chills when we see an elegant dancer flutter across stage on pointe, it should be an enthralling and educational experience.