The Joyce Theatre is Manhattan’s downtown, contemporary counterpoint to all the uptown tutus. But in late summer, when the city’s Swan Queens have flown upstate or migrated overseas, the Art Deco jewel box presents a ballet festival. Next Tuesday through Sunday, the Joyce Ballet Festival will focus for the first time on a single choreographer—Jerome Robbins. The guest curator is Tiler Peck, a senior ballerina of famed musicality at the New York City Ballet, where the works of Robbins and George Balanchine symbiotically coexist. For her Ballet Festival program, Peck has gathered together dancers she admires from N.Y.C.B., American Ballet Theatre, Paris Opera Ballet, Miami City Ballet, and the Royal Ballet. “I wanted to make sure that these Robbins ballets were danced by people who haven’t done them,” she explains. “Obviously, I wanted this program to be nice for the audience, but, selfishly, I wanted it to be beneficial for the dancers too. I wanted them to get debuts, to help them grow.” —Faye Arthurs