In 1995, the Fire Island Dance Festival began as a way to raise funds for those suffering from H.I.V./AIDS. Now entering its 20th season, the festival continues to expand its artistic ambitions. This year, it has commissioned a new work by the American Ballet Theater star Marcelo Gomes. Sara Mearns of New York City Ballet will dance with eight men while her fellow company member Troy Schumacher presents a work of his own. Other highlights include Ailey II in an excerpt from "Revelations," the dance star Desmond Richardson performing a solo, and hula dancing.