Oscar- and Golden Globe-winning actor Geoffrey Rush resigned Saturday as president of the Australian Academy of Cinema and Television Arts. The move follows allegations earlier in the week of inappropriate behavior, and comes just days before the academy hands out its annual awards. One of the world’s best-known performers, Rush has credits that include “The King’s Speech,” “Pirates of the Caribbean” and “Shakespeare in Love.” He won the Best Actor Oscar for “Shine.” The allegations against him emerged Wednesday when the Sydney Theatre Company revealed that it had received a complaint about Rush after he appeared in “King Lear” there...