As one of the world’s premier modern dance companies, Alvin Ailey American Dance Theater knows how to turn up the heat, playing to sold-out houses and ovations wherever they tour — including during their last visit to the NAC in 2007. With the most distinctive and extraordinarily well-trained assemblage of artists, the diverse company, under the leadership of new artistic director Robert Battle, performs mesmerizing works by internationally recognized choreographers. The company thrills audiences with its vibrant and joyful performance mix, celebrating the uniqueness of African-American culture. Ailey himself would be proud to witness his company today, revered the world over.