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Like Hong Kong, Taiwan has a tumultuous recent history and a diverse blend of cultures. What it doesn’t have is a mainstream cinema with the swagger, vitality, and pan-Asian appeal of its neighbor. Instead, Taiwan has nurtured the austere, arty style of such first-rate filmmakers as Hou Hsiao-hsien, Tsai Ming-liang, and Edward Yang. The third director, whose work has been little seen in Washington, gets a local introduction with this six-film retrospective, which opens with Taipei Story, a kaleidoscopic account of modern Taiwanese urban existence that includes a rare performance by Hou Hsiao-hsien (June 6 at 1 p.m.), and A Confucian Confusion, a comedy about cultural rootlessness (June 6 at 3:30 p.m.). Yang will introduce the screening of Mahjong (pictured), an acclaimed black comedy that also weaves a tapestry of urban life (June 13 at 3:00 p.m.). Other films in the series include The Terrorizer, in which a girl’s prank phone calls create crises in a variety of other lives (June 14 at 5:30 p.m.); A Brighter Summer Day, in which youth-gang rivalries in early-’60s Taiwan serve as a metaphor for social breakdown (June 20 at 2 p.m.); and That Day, On the Beach, in which a woman awaits the results of the search for her possibly drowned husband (June 27 at 2 p.m.). At the National Gallery of Art East Building Auditorium, 4th & Constitution Ave. NW. Free. (202) 737-4215. (Mark Jenkins).